Frank Wilczek has a new Reference Frame piece in this month’s Physics Today. It’s about the question of whether the parameters of our fundamental physical theory are uniquely determined by abstract principles, or “environmental”. He gives two reasons for suspicion about the idea that these parameters are calculable from a fundamental theory:

1. They have complicated, “messy” values and, despite much effort, no one has come up with a good idea about how to calculate them (an exception is the ratio of coupling constants in a supersymmetric GUT). He writes:

*Could a beautiful, logically complete formulation of physical law yield a unique solution that appears so lopsided and arbitrary? Though not impossible, perhaps it strains credulity.*

2. Some of the values are fine-tuned to make complex structures and thus life possible:

*It is logically possible that parameters determined uniquely by abstract theoretical principles just happen to exhibit all the apparent fine-tunings required to produce, by a lucky coincidence, a universe containing complex condensed structures. But that, I think, really strains credulity.*

Personally I don’t see the same degree of believability problems that Wilczek sees here. On the first point, it seems quite plausible to me that there are some crucial relevant ideas we have been missing, and that knowing them would allow calculation of standard model parameters, by a calculation whose results would have a complicated structure.

On the second, it’s not at all clear to me how to think about this. Sure, the fact that our universe has highly non-generic features means that it is incompatible with generic values of the parameters, but there’s no reason to expect the answer to a calculation of these parameters to be generic. I guess the argument is that there would then be two quite different ways of getting at some of these parameters: imposing the condition of existence of life, and a fundamental calculation; and if two different, independent calculations give the same result one expects them to be related. But the question is tricky: by imposing the condition of the existence of life in various forms, one is smuggling in different amounts of experimental observation. Once one does this, one has a reason for why the fundamental calculation has to come out the way it does: because it is has to reproduce experimental observations.

Wilczek avoids any mention of string theory, instead seeing inflationary cosmology and axion physics as legitmating the idea that standard model parameters are fixed by the dynamics of some scalar fields, or something similar. This dynamics may have lots of different solutions so:

*We won’t be able to calculate unique values of the parameters by solving the equations, for the very good reason that the solutions don’t have unique values.*

The fundamental issue with any such anthropic or environmental explanation is not that it isn’t a consistent idea that could be true, but whether or not it can be tested and thus made a legitimate part of science. It’s easy to produce all sorts of consistent models of a multiverse in which standard model parameters are determined by some kind of dynamics, but if one can’t ever have experimental access to information about this dynamics other than the resulting observed value of the parameters, why should one believe such a theory? It is in principle possible that the dynamics might come from such a simple, beautiful theory that this could compel belief, but the theories of this kind that I have seen are definitely neither simple nor beautiful. If you want me to believe in a complicated, fairly ugly theory, you need to produce convincing evidence for it, some sort of testable predictions that can be checked. Wilczek does believe that multiverse theories may provide such predictions:

*Of course, the very real possibility that we can’t calculate everything in fundamental physics and cosmology doesn’t mean that we won’t be able to calculate * anything * beyond what the standard models already achieve. It does mean, I think, that the explanatory power of the the equations of a “theory of everything” could be much less than those words portend. To paraphrase Albert Einstein, our theory of the world must be as calculable as possible, but no more.*

One can’t argue with this: if a model make distinctive predictions, and these can be compared to the real world and potentially falsify the model, one can accumulate evidence for the model that could be convincing. Unfortunately I haven’t seen any real examples of this so far. The kind of thing I would guess that Wilczek has in mind is his recent calculation with Tegmark and Aguirre that I discussed here. I remain confused about the degree to which their calculation provides any convincing evidence for the model they are discussing.

Unlike many theorists, Wilczek personally seems to be an admirably modest sort of person, and perhaps this has something to do with why the multiverse picture with its inherent thwarting of theorist’s ambitions to be able to explain everything has some appeal for him. Over the years during which particle theory has been dominated by string theory, Wilczek has shown little interest in the subject, perhaps partly due to its immodest ambitions. But I see two sorts of dangers in the way his article ignores the string theory anthropic landscape scenario which is what is driving the interest of much of the theory community in these multiverse models. As his advisor David Gross likes to point out, accepting this scenario is a way of giving up on the perhaps immodest goal he believes theorists have traditionally pursued, and one shouldn’t give up in this way unless one is really forced to. None of these models is anywhere convincing enough to force this kind of giving up.

The second danger is that what is happening now is worse than just giving up on a problem that is too hard. The string theory landscape anthropic scenario is being used to avoid acknowledging the failure of the string theory unification program, and this refusal to admit failure endangers the whole scientific enterprise in this area.

**Update**: It has been accurately pointed out to me that Wilczek does mention string theory briefly at one point in the article (“Superstring theory goes much further in the same direction”), and alludes to it at another place (when he talks about a “theory of everything”).

urs,

I’m not sure what the problem is, but the html that I see in your comment has the proper syntax for a text link, but with no text. Let me see if I can reproduce your problem

this is the link text.

Nope, can’t reproduce it., when I put in by hand the html code for a link, as above, it works.

Kea

It was John Baez literary simile (about how ants search for stuff by apparently random wanderings and citing each other’s papers so as to leave a scent trail). You have to ask him further questions about condiments–butter in particular.

Baez simile is in post #15 of this discussion-board thread:

http://www.physicsforums.com/showthread.php?t=121501

Come to think of it some ants go nuts over butter, don’t they?

Comments by Baez from the same time, on related topics (some category theory), are in this thread beginning at post #12

http://www.physicsforums.com/showthread.php?t=120985

Peter said

The invocation of Godel incompleteness is pretentious and absurd since there is nothing deep, subtle, or fundamental going on here. Lots of speculative ideas about physics turn out to be useless once you look into them because they canâ€™t be used to actually predict anything about the real world. String theory unification is just one more such useless idea, and the only strange thing about it is the sociological phenomenon of serious scientists refusing to abandon a failed project.That was nice đź™‚

-drl

TL said

It has been obvious to me for almost two decades which kind of new math is needed to quantize gravity; since spacetime diffeomorphisms play a fundamental role in gravity, we need to understand the diffeomorphism group and its projective representations.

You need to deal intrinsically with the volume element. This is what Dirac and GR have in common.

-drl

Aaron, you have my symphaties, since I have been in the same position myself; after completing a 4-year postdoc, I was unable find an academic position. I didn’t try very hard, though, since other priorities were more important to me at the time: staying in my home town, getting a permanent income, and starting a family. Leaving academia is not the end of the world; just about everyone I know who has been in a similar position have eventually landed on their feet.

Who Says:Bee wrote in a constructive simpatico spirit (IMO) as follows:

Or, to put it differently, someone should think about what we ought to do with all the String Theorists.

Well, I am a German social democrat. We don’t just fire people. We give them a second education, and a job so they feel useful. It’s called solidarity. The resistance to changes can be significantly lowered when there are as little people as possible suffering from it.

Alejandro Rivero Says:No, modern theoretical physicists are not driven (mainly) by curiosity, but by the joy of solving problems.

Not sure about that. There are certainly those who find joy in doing what they have learned and what they were educated for. But that’s got nothing to do with physics in particular. If I talk to people I often find that they were originally driven by curiosity, but they don’t dare to follow it cause it’s not career-wise. You wouldn’t believe how many people have told me, they would rather do this or that than following the main-stream, but they have to think about their job and family and stuff. That’s a problem which can only be solved by reevaluating which research is worth funding, and what ‘success’ means (imo certainly not getting a paper published).

Best, B.

Eugene Stefanovich Says:

It is quite possible to â€ślook for the sandwich â€ť and work for a software company (or a patent office) at the same time. This has a great advantage of being free to choose your own â€ścrumb trailâ€ť and stay out of the crowd.It depends whether you get exhausted by a demanding job as well as having other responsabilities. I am free enough to follow any path that I feel like, but almost no energy is left of me to explore things in a deeper level. So I am completely stuck.

Best wishes,

Christine

PW said: “The attitude of â€śLambchopofGodâ€ť encapsulates well everything that is wrong with what is going on in particle theory these days. The idea that â€śtoo much mathâ€ť is what caused the problematic state of the field has caused a backlash against investigating new ideas about mathematics and fundamental physics and this is both unfortunate and extremely unhealthy for the future of the subject.”

I didn’t say that “too much math” is the problem. I said that very mathematical investigations of the basics of string theory have been tried, as a way of pushing the subject forward. It has been tried, even, in my own insignificant way, by me. Eventually I was forced to admit that it didn’t work. Believe me, I would love to see some deep theorem in global differential geometry used as the basis of some vacuum selection principle. That would be wonderful. But things like that have been tried and they didn’t work. Now it”s time to try other things {like trying to bend ads cft to get it to say something about desitter }

The problem in particle physics is never too much mathematics, rather it is giving less physically suitable mathematics too much hegemonic power over physics.

There are of course some lucky historical circumstances, as the discovery of quantum mechanics, where, after the Born-Jordan observation of the role of infinite matrices in Heisenberg’s paper, the intrinsic logic led directly to Hilbert spaces and operators (interestingly enough it was first Fritz London and not John von Neumann who saw this first, but he was at the time a little assistant at the TU Stuttgard and his publication got easily overlooked by those who were leading the quantum dialogue); but the best situations for a happy marriage of physics and mathematics are those in which the mathematical and physical concepts developed at the same time and allowed to merge in an early state. The most perfect example (unfortunately little known outside a small circle of experts) is the birth of modular operator algebra theory from a confluence of vast generalization of the unimodular aspect of (the Haar measure) of noncompact group algebras into the heart of operator algebras, together with the physics ideas of Haag (leading to the Haag-Hugenholz-Winnink paper where modular properties are combined with the KMS condition) on how to do thermal quantum theory directly for open systems (see Haag’s book). This has recently led to the totally intrinsic (i.e. without the use of field-coordinatizations) concept of modular localization. In my whole professional life I have never seen such a perfect match and all my recent results and presently evolving ideas are around these new and mathematically quite demanding concepts in QFT.

There are also less fortunate marriages. In the middle of the 70s during a year at CERN there were some interesting mathematical properties showing up in low-dimensional QFT. This was the time when Euclidean methods in QFT were on almost everybody’s mind. Before I knew anything about Atiyah-Singer index theory, I observed a connection between Fermion zero modes and the winding number of the (generic) abelian gauge field in the Schwinger model (2-dim. massless QED). I had the intense feeling that I was dealing with a tip of an iceberg. But since I had no proof, those speculative claims of my seminar presentation which went beyond the concrete model calculations were rightfully criticized by Roman Jackiw. Only when I finally went down to the Geneva University library I realized that I had a very special case of an impressive mathematical edifice. I went on happily for several years, learning the mathematics of this new trade, but finally I began to have doubts whether such a (often banalized) use of the Euclidean is really the wave of the future in real time QFT. My doubts strongly increased when I came back to CERN after 10 years and saw all those enthusiastic wide-eyed yougsters using the phrase “topological” (this was after Atiyah-Witten) in almost every second sentence.

In contrast to Peter I am concinces that this of marrying precise mathematics with ever increasingly mataphoric physics was the beginning of the trip into stringlandia.

Lambchop,

I agree with you that new math is not going to solve problems like finding a specific string theory vacuum. Buth neither is any physical idea, since this is an inherently insolvable problem. What really bothers me is that instead of admitting this, people blame past failure on the mathematical methods being tried. It would be best if people would just move on to more promising problems, but if they’re not going to do that, at least trying out new mathematical methods sometimes leads to a useful new technique that can be applied elsewhere. Trying to get at the “physics” of a situation where there is none leads nowhere.

Bert,

My perspective is a bit different. I think there is still a huge amount to learn by pursuing ideas about TQFT and gauge theory, ideas that are completely independent of string theory. The problem with research in this area is that people will only fund it and pay attention to aspects of it that are somehow related to string theory. Studying those has led to some interesting things, but little recently. The non-string theory connections to gauge theory are quite worth exploring, but no one wants to since it’s a hard, long-term research project which no one wants to hear about because it’s not string theory.

Of course there is Peter, in fact I am exploring problems (massless, spin1 and 2), but already the preliminary results creates doubts whether the historical name (which is primarily a classical name) “gauge” is very appropriate.

On the other hand names in particle physics are increasingly hollow words and if you mean the physics behind the word gauge theory (in particular the physical, alias gauge invariant results) then we are on the same wave length. In fact I am probably much more conservative on the side of physics than you are, but I am upholding the right to use any mathematical concepts which are the most appropriate to implement the physical principles (which only change on scale of one century) and concepts and I happen to think that the present formalism of gauge theory does not meet this test (see my remarks I made earlier, giving support to Thomas Larson in Fantastic Realities, probably more radical than what he had in mind).

B:

”

Or, to put it differently, someone should think about what we ought to do with all the String Theorists. ….

Well, I am a German social democrat. We donâ€™t just fire people. We give them a second education….

”

A nuclear physicist by education who now does “phenomenological quantum gravity” teaches string physicists what to do after their project has failed? By all means, they can’t wait to hear!

This is getting more absurd every time I read around here.

Since Newton age (and even Democritus and Archimedes!) this needed “new math” has been a new math related to the understanding of geometry, particularly of differential geometry. The key word here is not “new”; it is “understanding”. Advances in physics are related to our understanding of geometry. This close marriage is maintained in the algebraic side via some dualities, for instance the one between commutative algebras and manifolds.

Advances in string let to set up and solve new problems on mathematics, and even create new mathematics, but it is still to be seen how they help to understand any branch of mathematics, nor to say differential geometry.

Alejandro,

Nobody is against geometry, but it has to come from the midst of raw local quantum physics rather than offering a geometric/topological mathematical (or classical physics) stick to particle physics to jump over.

IMHO playing with math models and hoping to find something interesting about physics is equivalent to “searching the key far from the lamppost”. The chances of finding the key are very slim. I would rather get the clues about physics from … well, physics. More precisely, from experiment. Try to build your theories by only using concepts and ingredients that are (at least, in principle) experimentally measurable. Reject quantities that have no observable counterparts in nature. For example, I would not hesitate to throw away gauges. They have no observational meaning by definition.

Nobody is against geometry, but it has to come from the midst of raw local quantum physics…Which is precisely why the category theoretic understanding of local geometry is the

onlyway forward.The AQFT papers that I have glanced at recently all talk about functors from some suitable category of (local) spaces, such as the category of strongly causal manifolds. Where exactly do you think this is leading?

Kea,

your observation is not quite correct. Categorical ways of arguing were actually used by people who you would not exactly count as algebraic QFTists as e.g. Moore and Seiberg in their approach to the structural properties (related to the new braid group statistics) of chiral observable algebras and their superselection structure In a paper “Einstein causality and Artin braids” which was written at the same time and addressed the same problem (by Rehren and myself) we extract this structure from a new manifestation of the old causality principles which was in a AQFT spirit without any use of categorical arguments (afterwords this spirit was strengthened in collaboration with Fredenhagen who had more experience with AQFT methods).

However categorical arguments are sometimes an ultimate recourse (as in the case of the formulation of the local covariance principle in QFT in CST to which you are referring) and should be considered (in my view) as tentative to be replaced by more geometrical arguments. But when I do use the word geometric, I do not mean that kind of geometry coming from classical physics via quantization (Chern-Simon geometry, geometry of euclidean functional integration manifolds etc) but rather those geometric concepts which AQFT manages (e.g. via modular localization) to extract directly from the autonomous local quantum physical principles, and which in all cases up to now amounted to a widening of the scope of causality and spectral stability principles and not to their “revolutionary” liquidation.

There is a big difference between this geometry from AQFT and that e.g. in the Atiyah-Witten (or for that matter string theory) setting.

But when I do use the word geometric, I do not mean that kind of geometry coming from classical physics via quantization…but rather those geometric concepts which AQFT manages (e.g. via modular localization) to extract directly from the autonomous local quantum physical principles…And if I might be permitted to repeat my question: what is the geometric language for these geometric concepts?

Kea, let me try to give an answer to your question inasmuch as this is possible in a weblog.

The modular operator theory is capable to extract spacetime localization from the abstract domain properties of the modular objects related to an operator algebra. The abstract (algebraic) relative positions of operator algebras acting in a common Hilbert space leads (via that modular theory) not only to spacetime symmetries but also encodes the full content of QFT (statistics, inner symmetry, scattering theory…). The theory is pretty much in its beginnings and some of the results may seem miraculous (especially to those who thought that Lagrangian quantiation contains alrady the main messages about QFT) but any mysterious appearance is transitory (simply due to unfamiliarity) and its aim is to de-mystify and it is not to be thought of as a theory of everything. From a pure mathematical point of view it is somewhat related to Vaughn Jones theory of inclusions (subfactors), but the involved algebras are of a different type which is inexorably linked with localization (in my papers in http://www.lqp.uni-goettingen.de/papers/06/04/ I have called that kind of algebra “monade”). If you are interested in some partial results of an ongoing research have look at math-ph/0511042 where there are also references to previous work.

Its main message is perhaps that if a more than 70 years old theory allows for such a radical different approach, it is not (despite the string theoretical carricatures of QFT) yet anywhere near to closure.

Dear Bert

I do not doubt for a moment that what you claim is true. It sounds fantastic and exciting. It does not, however, answer the question. You used the word

algebrafive times in the above statement. Perhaps we could begin with a clarification of one single term: what do you mean bydomain property?Although the algebras which feature in those constructions are algebras of bounded operators, the Tomita involution S`(see the mentioned literature), which is a kind of master operator capturing collective properties of all operators in the algebra, is unbounded and its domain of definition is (in the field theoretic context) related to the geometric localization of the algebra. The problem is that this deep mathematical theory has not entered any of the standard mathematical physics books (Reed-Simon,…) but it is explained in the cited articles and their references. A nice little introductory mathematical article can be found on Steve Summers homepage. Please do not expect that such a mathematical subtle and conceptually demanding theory allows an instant packaging in an weblog. The only thing I can do here is to say that it exists and already in its present incomplete form it gave profound physical results.

Would that be the same Steve Summers who cites Baez, Doplicher, Roberts and Redei?

Yes it is the same. Among the recent online collection of articles you find a 10 page article with the title: Tomita-Takesaki modular theory

It is probably also available on the math-ph server. Most of the very recent physical results are however not contained. But your question of how and what kind of geometry emerges from the algebraic positioning of operator algebras is briefly explained and you will be referred to more detailed literature.

A link to the Summers paper

I’m looking through it, at theorem 5.2 for instance, where he says the modular unitaries generate a representation of the group of isometries of (2D) Minkowski space. I’m a little confused. For some reason I thought the

geometryof these wedges and things should be written down in the language of sheaf cohomology.Eugene,

When the atomic constitution of matter was first postulated was it

knownto have observable counterparts in nature?The point of view you express is close to that attributed to Ernst Mach. Mach never accepted atomism, and had little use for relativity.

Einstein, despite being influenced by Mach, ultimately concluded that it is the theory we are attempting to test that says what might be observed. It provides a framework for motivating the operations that give rise to observations, as well as specifying the expected features of those observations.

I would rather get the clues about physics from â€¦ well, physics. More precisely, from experiment.Physics has never been simply about getting clues from experiment. It has always had a metaphysical component—again, something that Einstein understood well. However, insofar as it is about experiment it is about understanding stable, reproducible observations. Indeed, in a deep sense it is about the possibility of stability itself. I believe this leads inescapably to a profound reflexivity in the foundations of physics, because if one employs invariant laws to account for stability—or reproducible patterns—one is eventually led to inquire into the stability and success of the laws themselves. I would define physics as this seeking after stability, both stimulated and constrained by controlled observation. This effort has been enormously successful. The question is, why should nature—or existence—accommodate such success in seeking after stability and principles of invariance?

The currently popular incarnation of the anthropic principle gives a trivial and ultimately sterile answer to this question: The Multiverse is so vast and diverse that it accommodates anything—environments where stability can be found, and not incidentally, where life and science can exist, and a vastly greater array of environments where such is not the case. The fact that we exist in an environment where stability can be discovered is from this viewpoint a simple matter of selection; if we didn’t, we wouldn’t be discussing the topic or have a civilization based on the possibility.

In contrast to such sterility, can the reflexivity explained above point the way to an genuine advance in theoretical physics? That is, can physics advance by reflecting on itself, bearing in mind that what calls for explanation is in part the prior success of physics? (Remember that this kind of consideration is what motivates correspondence principles.)

Bert

Why did you choose the term

monade?Kea,

this time the answer to your question is well suited for a weblog.

One reason for substituting the full mathematical name: hyperfinite type III_1 Murray-von Neumann factor algebra by something shorter (in a paper where it occurs many times) is that it is very unwieldy. Writing simply HTIII_1FA is ugly. In looking for a word which reveals something about its conceptual aspects the word “monade”is very appropriate for two reasons. A single such mathematical object is unique i.e. up to isomorphism there exists only one, i.e. it is analogous to a point in geometry. The situation changes radically when you place several copies of this unique object (as operator algebras) into a common Hilbert space; with a carefully chosen positioning dictated by “algebraic naturalness” based on modular operator theory (modular inclusions, modular intersections), you create the rich world of QFT in Minkowski spacetime (including spacetime and inner symmetries) where all the differences between QFT models have their origin only in the huge cardinality of possibilities of modular positionings (to generate chiral theories you only need 2 copies, for 4-dim. QFT the minimal number is 6). This is precisely the quantum physics realization of Leibnize’s monade theory of how reality originates from the relative positions of “monades”, in fact it is a perfect match (but you had to go up to local quantum physics to find it).

The mathematical physicist who discovered some mathematical properties of this positioning (Wiesbrock, you can find some of his papers he wrote in the 90s in math-ph) could not continue his career; he had the bad luck of living at the wrong time (a time when academic priority was given to string theorists). Most mathemaical Field medalists (exeption Vaughn Jones, Alain Connes) do not know this mathematics; it comes to a large part from a string-free zone in particle physics.

When Haag was travelling through Princeton and met Witten, this issue came up in a conversation; but it seems that Witten apparently dismissed it, probably because he and Atiyah were convinced at that time that real particle physics had to come through the massaging of that (nonexisting) functional integral.

Recently I succeed to obtain 3 quite interesting (published) result using modular methods

1) A very clear understanding of the recipes underlying the construction of factorizing models (including the spacetime interpretation of Zamolodchikov-Faddeev algebras).

2) Together with Mund and Yngvason we finally understood the best localization aspects of the infinite spin Wigner representations (besides the massive and the finite helicity massless representations the third big family of potentially physical representations) and the string-localization of potentials associated with massless finite helicity fields and their mild short distance properties (which makes them ideal candidates in the search for renormalizable islands in the infinite parametric space of the renormalization group)

3) A deep quantum understanding (a modular version of holography) of the infinite dimensional mysterious Bondi-Metzner-Sachs group and of the the close connection of the Volume law of heat-bath created entropy with the area law caused by vacuum-fluctuation at the boundaries of causal localization (as already mentioned in http://www.lqp.uni-goettingen.de/papers/06/04/ ).

There will be a forthcoming paper by Gandalf Lechner from Goettingen (his thesis) where he succeeded to proof the mathematical existence of factorizing models (the solution of the old nontriviality problem in a still limited context). These models, unlike those superrenormalizable in the book of Glimm-Jaffe, are for the first time only strictly renormalizable.

Together with Jens Mund and Jakob Yngvason I am presently working on a renormalized perturbation theory based on those string-localized field (absolutly nothing to do with string theory). A little note on the string-like potential describing the metric tensor will appear in a little separate communication by Mund within the next two weeks. We are under the impression that within this extended perturbative framework gravity will be renormalizable (finite-parametric) or to phrase it more carefully: the massless higher helicity string-localized potentials permit renormalizable interactions.

I just realized that I forgot to mention a result obtained in the algebraic modular setting which will probably interest many participants in this weblog beyond Kea

The idea of modular Euclideanization (as opposed to Osterwalder-Schrader Euclideanization of real time QFT) leads to a structural proof of a temperture-duality of thermal correlations (hep-th/0603118 and literature quoted therein) for chiral theories of which the Verlinde duality arises from the zero-point correlation function (the partition function or character of loop-groups). As its higher dimensional analog the Nelson-Symanzik duality it is a manifestation of the structural richness of the implementation of the causality principle of local quantum physics. In fact it is much richer than the N-S duality, because it generalizes the Victor Kac observation:

representation theory of loop groups –> identities for modular forms

to:

causality principle for chiral theories –> identities for modular forms,

with other words the totally autonomous modular concept arising from the T-T modular theory of operator algebras contains the concept of modularity of so-called modular forms (all those funny Ramanujan-kind of identities have a common structural root: the causal locality principle of QFT!). And mathematical physicists have a fare share of this modular theory because important concepts as the KMS property (which Connes used for classifying the type III factors which brought him the Field medal) are due to physicists. Although physicists work in a more special context, it would not have been propostorous to call it the T-T-H-H-W (adding Haag, Hugenholz and Winnink) to the list of protagonists.

Kea if you are really interested and you would live in Brazil, I would recomment to attend a Sattelite meeting down in Floripa at the end of July:

http://www.mtm.ufsc.br/~exel/oa/

In normal times such insights would be of interest to more mathematicians, but remember that this is coming from a string theory-free zone.

For those who are having difficulty getting research jobs,

have you considered lecturer positions? These are usually

not too difficult to find, and while the pay is not great,

you typically have summers free for research, and usually

less administrative responsibilities than you would have

in a tenure-track position.

I’ve noticed lecturer positions seem to be a mixed bag for the most part.

At some places, they seem to be term contracts which have to be renewed every term or year. In some cases I’m aware of, some lecturer contracts were not renewed because of things like departmental politics. Popular “excuses” for not renewing were silly things like too many poor student rewiews and/or complaints, frequently used by the department to get rid of folks they don’t like.

In some departments which had an emphasis on research, the lecturers are treated as 2nd class citizens or “bottom feeders”. At a community college, the problem seems to be things like students not wanting to be there and goofing around too much. (The sad part about some community colleges, is that a large number of lecturers there were actually folks who did not get tenure at a research university. Some of these folks seemed quite miserable for the most part).

Though on the other side of the coin, most lecturer positions had very little to no bureaucratic and/or management duties outside of teaching. For many of my previous colleagues which have tenure at a university which emphasized research, their number one complaint was all the bureaucratic duties they had to deal with. In that sense, it wasn’t much different than working in a Dilbert style corporation.

Bert Schroer, Kea,

lest the impression arises that Tomita-Takesai theory, von Neumann type III factors and the like play no role in string theory, let me point out the work by Stolz and Teichner, who are in the process (for quite a while now) of giving a geometric interpretation of elliptic cohomology

( http://golem.ph.utexas.edu/string/archives/000737.html )

in terms of CFT with target some string bundle

( http://golem.ph.utexas.edu/string/archives/000799.html ).

See for instance page 53 of this review

( http://golem.ph.utexas.edu/string/archives/000712.html )

to see all the machinery – that Bert Schroer mentioned – in action.

Urs,

that is not what I meant. The von Neumann algebras e.g. in the last part of the first article are just an epiteton ornans (ornamental addition copied from Wassermann’s article) to the main text.

The setting of the authors is that of Greame Segal’s axiomatics of (topological) Euclidean field theory, which has only a metaphoric relation to a similar real time axiomatics a la Brunetti-Fredenhagen. What I really meant is an Euclidianization of the T-T modular theory in the Nelson-Symanzik duality tradition which in the chiral setting is a modular analog of the Osterwalder-Schrader Euclideanization (i.e. something which comes from our past in autonomous particle physics i.e. which was there before the Atiyah-Witten era). With other words something which is in the tradition of modular theory a la T-T-H-H-W (a terminology which I explained before) enriched with the notions of modular inclusions and modular intersections (which are essential for my use) which were discovered in the 90s by Wiesbrock before he had to leave academia. One glance at that work on modular holography (mentioned before) would show you that we are talking about completely different conceptual setting which just happen to share a few common references.

Please don’t fall prey to the trick in string theory to claim huge areas and semantically incorporate it (a phenomenon which was discussed before with Peter). Since you are a member of a mathematics department you have all the right to be interested in elliptic objects, but I think as a particle physicist I have the right to be proud of our rich and almost forgotten traditions and to use them in a new context (and fight any insinuations that this has grown on the soil of string theory)

Dear Peter,

just to get away from that long discussion with various participants on this webblog for a change, I would like to make some personal comments.

Since I was a newcomer to your weblog at the time of its third birthday, let me congratulate you for your fulltime work of managing this weblog so successfully. I hope the physics Columbia university physics department realizes what a useful role this string theory critical weblog plays in very precarious times for particle physics (I think even string theorist can see this point).

As you certainly have realized, we have quite different opinions on what could help particle physics in this situation. But there is no hegemonial claim in either of our viewpoints.

When I listened to these three University of Princeton tapes of David Gross I was shocked by his salesmenship of semantically manufactured facts (described before in a contribution where I quoted from original papers of string theory). We always think of George Bush, when we talk about manufactured facts. Well, it happens in our midst and the intellectual creme of Princeton University is applauding. I also was appalled by what he said about LQG although (contrary to you) I have a somewhat critical position with respect to LQG (and I think some of the questions and comments referring to Lee Smolin are justified; also I do not want to see particle physics and in particular gravity end in an Armegeddon between LQG and string theory). Since I could not believe that a place where I spend some time in the 60s had now fallen so low, I searched for other videotaped talks. I listen to the first talk in 3-talk series by Mark Juergensmeyer with the title: “God and War: The Odd Appeal of War” (also a professor from Santa Barbara) and my view about Princeton was instanteneously corrected; the problem I had is really constricted to particle physics and may also occurs at other ivy league places which have a tradition for such talks.

We probably also agree that it is somewhat disappointing that such a integer and generally critical mind with a Nobel stature as Frank Wilszek does not take a more pointed position with respect to these strange sociological hegemonic manifestations. But then Gross was his thesis adviser, and in addition not everybody has that critical independent mind as Pauli (he was not always right, but he always fought for the coherence of physics and not in order to sell his own ideas).

I have a bottle of red wine on my table (this time from Mendoca, Argentinia) and I am in this moment drinking to your successfull continuation of this weblog. May people recognize what a hell of work you have to do in order to permit yourself some satisfaction.

The impression that algebraic quantum field theory is closer to phenomenological physics than to pure math, at least in comparison to other parts of “formal high energy physics” is something that I have not obtained.

Maybe its just me being ignorant (which I am, in a huge number of respects). But the worthwhile applications of AQFT that I have seen have precisely the status of physics-inspired math which Bert Schroer is so critical of.

The understanding of representation theory of loop groups and related CFT technology using AQFT techniques would be one example. Some math that people like Michael Mueger are doing

(as in his second talk here http://golem.ph.utexas.edu/string/archives/000711.html)

would be another.

I am also not sure why Minkowski-spacetime field theory is so much more “physical” or “real”. Sure, in some sense. But CFT applied to statistical mechanics is a Euclidean field theory. Any concept of field theory we have should be able to deal with Euclidean and Lorentzian backgrouds.

But (correct me if I am wrong) Minkowski spacetime and lightcones are build into the very axioms of AQFT. That looks like too strong an axiom to me.

MoveOnOrStayBehind Says:B:

“Or, to put it differently, someone should think about what we ought to do with all the String Theorists. â€¦.”

A nuclear physicist by education who now does â€śphenomenological quantum gravityâ€ť teaches string physicists what to do after their project has failed? By all means, they canâ€™t wait to hear!It’s not up to me to judge which research fields are promising. I just say, that it’s definitely necessary to objectively evaluate the situation. There are people who have sufficient knowledge and overview to give advise. Listen to them. I wouldn’t even say string theory has ‘failed’. But its over-rated.

I – in person – am certainly not the one to teach string theorists something besides phenomenological quantum gravity – if they are interested, I would love to do so! I can’t avoid noticing that String Theorists speak ‘stringy’ and someone has to make the translation. The quest for the Theory of Everything has quite some similarities to building the Tower of Babel.

This is getting more absurd every time I read around here.Dear MoveOnOrStayBehing: You got to move on – or stay behind…

Best, B.

Urs,

Loop groups are of course a valuable illustration, I mentioned the that the relation of chiral field theories with modular forms was first discovered in the context of loop groups (Victor Kac…).

The point here is that you do not want to invent a special drawer in which you keep loop group or general chiral field theory separated from the rest of QFT. The only interest in chiral quantum field theory is as a theoretical laboratory to learn something about the nonperturbative subtleties for higher dimensional QFT and for this reason you have to use those structures which are in common to QFT in all spacetime dimension (and that is modular localization). All special structures for families of chiral theories like loop groups (sorry, for me they always remained current algebras) have been investigated or can be investigated by mathematicians, hence why should I loose time in getting into competitions with them? What I can contribute is the update or adaptation of some rich ideas from the past (and largely forgotten, just because you were so busy learning loop-groups and elliptic objects that you had no time to learn anything about the important conceptual past cross roads in particle physics, this is not a personal criticism). The Euclideanization of the modular group which underlies the (field-coordinatization independent) concept of causality and localization in the context of the chiral setting (without specializing to loop groups or other rational families) and which is in complete analogy to Nelson-Symanzik and Osterwalder-Schrader is something to the heart of a particle physicist like me.

I am not negating that for special families you can use other special methods coming from mathematics e.g. the vertex operator formalism of Graeme Segal, which has recently been used by Hu in order to derive the Verlinde formula for a special family (which is characterized in terms of vertex concepts which I am not familiar with (i.e. I do not know their precise relation to Wightman fields, to clarify this would be the obligation of the vertex algebra people because Wightman fields are much older).

I think that particle physics has a strong historical component which has been damaged because in the late 70s people (with the increasing arrogance of people entering math. phys. they never cared to look back whether some of these ideas already existed so that the already existing terminology could be taken over and enriched by new insights instead of cutting off the link to the past by a new terminology).

It is just as with human history, if you forget and surpress it, it will create confusions and conceptual regress.

Urs, your attempt to separate me from my colleagues of AQFT will not succeed, the past is too strong and even my present influence on what is going on in that community is not negligable.

I have a bottle of red wine on my table (this time from Mendoca, Argentinia)Oh! I was in Mendoza a few years ago. Lovely place. I would love to come to Brazil, but alas my poverty forbids it. Thank you, Bert, for taking the time to tell us a little about AQFT. Personally, I am 100% on your side, as regards the relevance to particle physics in comparison with Strings. I had a look at your beautiful paper on wedge localisation last night. Actually, Jones said a few words about his ideas on physics at a conference I was at recently, but unfortunately, as an organiser, he was not given the time to speak about any details.

My point is that certain instances of the category theoretic

monadshare many of the deep properties that you attribute to your monade. I do not think that this is a coincidence. Not all people looking at higher category theory are in the String camp.Here is a paper by Halvorsen on AQFT, with some category theoretic input.

Try again: paper

Kea,

of course higher category theory is not the domain of string theory. The first who introduced nonabelian cohomology and higher categories into QFT was John Roberts (in the middle of the 70s). He had a strong physical motivation coming from gauge theories. Things did not work out in the way he expected. But fortunately this was at a time when negative results on deep problems investigated with the best available tools were equally important and interesting Ă¤s positive results (somehow related to Pauli’s “not even wrong”) and so the work was published. I have the impression a negative result on string theory will not be tolerated by the community in fear of endangering the veracity of the whole construct. I am surprized that his work was not mentioned in recent string theory blogs. Street, who is the father figure in Australian n-category research always referred to it.

Returning to Urs:

where did I claim that AQFT is anywhere close to phenomenology? I said that it is directly related to the (utterly successful) principles underlying QFT (which are the condensed form of past experiments), more explicitly the principles together with some mathematical concepts to implement them. In a situation where you are stuck (hopefully only temporarily) on the experimental side, you are not condemned to do speculative blue yonder physics, rather there is the third way: press the principles and the concepts real hard and see what you are led to. But this is very difficult and time consuming and I cannot advise a young man under actual social physics department conditions to go into this since it is very risky for making a living (but there were some people who were willing to take the risk and a very few succeeded).

Urs, you mentioned Michael Mueger. Despite his beautiful conceptual work on order/disorder variables (and the fact that he is very talented) he could not get a position in physics. For quite some time he worked under Turaev in Strassbourg and it is natural that he looked at the more categorical aspects as they were investigated at the mathematics department of that university. He finally got a permanent position in Holland (probably in math.). Please don’t msiunderstand me, I am in no way against categorical settings and topological field theory. I only think that if this is already being done at mathematics departments it should not also be done in physics departments. Or to put it into a milder formulation, if it is done at a physics department the individual using it should at least be aware that the first topological field theory was that extraction of a tracial (combinatorial) algebra which carried the representation of the statistics operators in the DHR work on superselection sectors (see Haag’s book) and which was later discovered in a much more general setting by Vaughn Jones and called by him extremely appropriatly the “Markov trace” (where Markov refers both to the 19 century Russian probabilist and his son who stands for the braid group aspect). Whereas the topological bones can be perfactly placed into such tracial hyperfinite type II algebras as Vaughn uses them, this is not possible for the localizable and transportable meat.

Kea you said that you saw Vaughn Jones recently, is he well? We are all looking forward to see him in Floripa.

You know, if we’re judging string theory wanting for having produced little connection with the real world in the last twenty years, how should we judge AQFT having produced not a single example of a realistic QFT since at least the seventies.

Judge it by the results I mentioned this morning (at least something, it is not a theory of everything). In addition AQFT shares all the previous successes of QFT (including all the cross sections and vacuum polarization effects) because it is nothing but an vast conceptual extension (often with a more profound interpretation).

I would repent most of the things I said if string theory would only lead to a fraction of those results.

String theory is not an extension of QFT because the prerequisite would be a structural compatibility without which the standard scale-sliding argument is not worth anything. I have explained this in detail before in some older contribution and I am not going to repeat this here again.

You may not agree with me, but you certainly have to admit that at least it does not wipe out knowledge (which string theory has done and is still doing).

AQFT shares all the successed of QFT? What nontrivial theory in four dimensions has been constructed via AQFT?

Please donâ€™t msiunderstand me, I am in no way against categorical settings and topological field theory. I only think that if this is already being done at mathematics departments it should not also be done in physics departments.Bert, the people working on fractional QHE, for instance, have hardly been doing nothing for the last 20 years.

There are

engineersand computer scientists doing TFT mathematics. The question you should be asking is: how can I link this beautiful edifice of AQFT to what they are all doing?I was under the impression that solid state physicists cherish localized states and material properties and they need the localized carriers of those topological quantum numbers and not just their bones to make trustworthy calculations. Are you sure that you are talking about professional condensed matter physicists? Is among the physical results anything which would impress e.g. Phil Anderson?

To Aaron: if standard QFT would be able to construct a 4-dim. QFT it would be immediatly inherited by AQFT according to the logic I explained. I think you mean by “construct” something entirely different. I do not mean being able to write a functional integral, compute some renormalized Feynman diagrams and put some instantons on top, I meant mathematically controllable model constructions as they have been done in any other area of theoretical physics.