Thomas Love pointed me to a wonderful article from last year by Rudolf Haag. It’s more or less a short memoir of his scientific career, entitled Some people and some problems met in half a century of commitment to mathematical physics. There’s a lot about the history of mathematical physics related to quantum field theory that I learned from the article, which covers the second half of the twentieth century. Haag started out his career heavily influenced by Wigner and his work on representations of the Poincaré group, investigating what this had to do with quantum field theory. He has been one of the leaders of the operator algebra approach to formulating QFT.

His comments about the Witten and string theory bring back memories of the late eighties, when several people told me of similar experiences. Haag writes:

I had been asked to give a physics colloquium talk about my views on quantum gravity and hoped to have some discussion with Ed Witten. Next morning he greeted me by saying: “Your talk was very interesting but I would really advise you to work on string theory”. When he saw the somewhat incredulous look on my face he added “I really mean it. I shall send you the manuscript of the first chapters of our book”. This ended our discussion. Back in Hamburg I received the manuscript but it did not convert me to string theory. I remained a heathen to this day and regret that meanwhile most physics departments believe that they must have a string theory group and have filled their vacant positions with string theorists. To be precise: It is good that people with vision like Ed Witten spend time trying to develop a revolutionary theory. But it is not healthy if a whole generation of young theorists is engaged in speculative work with only superficial grounding in traditional knowledge. In many popularised presentations the starting point of string theory is explained as the replacement of the fundamental notion of “particles” with its classical picture of a point in space or a world line in space-time by a string in space respectively a two-dimensional worldsheet in space-time. This, I think, is a misunderstanding of existing wisdom. First of all, paraphrasing Heisenberg, one may say “Particles are the roof of the theory, not its foundation”.

Thanks for introducing haag’s writing.

In his writing, I notice these sentences that First of all, paraphrasing Heisenberg, one may say “Particles are the roof of the theory, not its foundation”.

Could anyone say what this means in detail?

younghun,

See the more detailed comments about Heisenberg and S-matrix theory at the bottom of page 272 and top of page 273.

IMHO, Haag’s most powerful statement comes a few lines later:

String theory is hailed as the most promising among present endeavours. But it is

an overstatement to call it a theory. It has not settled down to a well defined formalism

nor has it explained any existing puzzle nor can I see that it can make contact with

any observable phenomenon in the foreseeable future.

Thanks Thomas,

I should have included that quote too…

I thought the S-matrix was invented by Wheeler in 1937. Did Heisenberg actually anticipate Wheeler?

Peren, According to Wikipedia:

“S-matrix theory was proposed as a principle of particle interactions by Werner Heisenberg in 1941, following John Archibald Wheeler’s 1937 introduction of the S-matrix.” So Haag’s memory is faulty.

Haag won the 1970 Max Planck medal. Has anyone compiled a list of criticisms of string theory from Planck medal winners?

A link to SpringerLink? This (not even a paper, just a reminiscence) is stored behind a paywall, not at arxiv? Not cool, Haag, and not cool for linking to it, Peter.

Columbia and other US institutions may get free access to everything on SpringerLink, but the rest of us are not so lucky. A great advantage of physics over other fields is that we have rather more arxiv and rather less SpringerLink, and this is maintained in part by letting those who use SpringerLink rather than arxiv know just how much scorn and contempt we have for them.

younghun park said:

A simplified and short explanation: The starting point of AQFT is a net of operator algebras which contain all observables of a given QFT as selfadjoint elements fulfilling a certain set of axioms. This is the only input to the theory, so you could say that AQFT is quantum field theory without fields. Fields may be used as an auxilliary device to construct the net of observables, but they are no necessary ingredient.

The philosophy of AQFT is to derive every other concept from the net of observables, including the particle content. The concept of a particle as a point in space or as a worldline in spacetime does not enter the theory here. Instead, it is a theorem that the algebra of observables of a point of a spacetime is necessarily trivial, which means that AQFT already says that the concept of a pointwise localised particle is oversimplified.

Furthermore, the Reeh-Schlieder theorem says that there cannot be a localized particle number operator, which means that the question “how many particles where in a certain time interval in a certain box” is meaningless in AQFT.

For more information I would like to recommend the nLab as a starting point:

http://ncatlab.org/nlab/show/AQFT

Alas it is behind a paywall.