Chen-Ning Yang (often known in the US as “Frank”) passed away in Beijing yesterday at the age of 103. He was the last of the great figures of 1950s high-energy particle physics still with us.
His name is associated with two of the central ideas of what was to become the Standard Model.
- In 1953, together with Robert Mills, he wrote down the extension of the theory of quantum electrodynamics from the the case of gauge group U(1) to that of SU(2).
- In 1956, together with T.D. Lee, he argued that the weak interaction theory should (very unexpectedly) be one that violated parity conservation.
The original Yang-Mills theory was supposed to describe the strong interactions, with SU(2) isospin symmetry. This idea doesn’t work, but later on the SU(2) Yang-Mills theory became the foundation of the unified electroweak theory. Extending from SU(2) to SU(3), one gets the rest of the Standard Model, QCD.
The problem with Yang-Mills theory in the 1950s was that, treated perturbatively, the photon of QED gets replaced by a triplet of spin 1 massless particles, but there is no such thing in nature. Unlike the photon case, this triplet will have self-interactions, and the hope from the beginning was that these would explain away the lack of massless particles. One way to get rid of the massless particles is the Anderson-Higgs mechanism, first described by Anderson in 1962. For Anderson and others working on this, the hope was to use a spontaneously broken SU(2) gauge theory to describe the strong interactions. Only later, in 1967, was this idea applied to unified electroweak models.
The other way to get rid of the massless particles is to realize that while the quantum Yang-Mills theory is asymptotically free at short distances (where massless states are relevant), at long distances the self-interactions become large and the spectrum of the theory has only massive confined states. Moving from SU(2) isospin symmetry to SU(3) color symmetry, one finally got (1973) a very successful Yang-Mills type theory of the strong interactions.
While the Yang-Mills proposal for the strong interactions took 20 years to come to fruition, things happened very differently with the Lee-Yang proposal of parity non-conservation. Lee and Yang submitted their paper about this on June 22, 1956. At the time Yang was visiting Brookhaven for the summer, coming into New York to work with Lee. A good place to read about this is here (with more here), which has:
Yang did not remember precisely how the idea of examining the previous experiments on weak interactions came to him and Lee, but he remembers when and where. It was early in May, and it occurred just after he had driven in to New York from Upton to visit Lee. He had picked up Lee at his Columbia office and was having difficulty finding a parking place near Columbia. He and Lee were driving around looking for one and talking. They finally parked the car temporarily in front of a Chinese restaurant near the corner of Broadway and 125th Street. The restaurant was not yet open, so they went into the White Rose Café nearby. They sat down at a table and resumed their conversation, and it was then that the idea struck them. It was suddenly clear to them that the results of one weak-interaction experiment after another had to be examined to see if they gave any information on parity non-conservation.
A Columbia colleague, Chien-Shiung Wu, soon started an experiment using cobalt-60 and had experimentally demonstrated parity non-conservation by December. Another Columbia group with a muon beam quickly showed parity non-conservation in that context. Not much more than a year after their paper, Lee and Yang received the physics Nobel Prize for 1957. This was definitely a high point for the Columbia physics department.
In 1966 Yang left Princeton for Stony Brook, where he founded the Institute for Theoretical Physics. By the time I arrived there much later as a postdoc (1984), Yang was very much an elder statesman of the field. I only remember talking to him a couple times, both not about science but about administrative issues.
The ITP shared a building with the math department, which had become a world center for geometry starting with the arrival of Jim Simons in 1968. It’s fascinating to hear (see here) the account by Simons and Yang of their attempts to understand each other’s language and their slow realization that the gauge fields of Yang-Mills theory were the geometer’s connections on a principal fiber bundle. Yang wrote a paper with Wu giving what became known as the “Wu-Yang” dictionary relating the two subjects. Singer learned of this when visiting Stony Brook, then brought the news to Atiyah in Oxford, starting an explosive development during the late 1970s.
Yang retired in 1999 and returned to Beijing. In recent years he has been involved in debates over whether China should build a new large collider, taking a rather skeptical view. For an extensive discussion of this, see here. Already in 1980 (see here) Yang had come to the conclusion that particle physics was not going to again see anything like what had happened in 1956: “the party’s over”.
So, on the spur of the moment, I said to Marshak, “Yes, I will say something, if you promise not to publish it.”
He said OK, and he stuck to his word later.
So I said, “In the next ten years, I think the title of the panel was either the future or the next ten years of high-energy physics,” I said, “In the next ten years, the most important discovery in high-energy physics is that ‘the party’s over’.” After I said that, there was general silence. Nobody said a word, and then Marshak declared the panel was finished.
I fear that developments since 1980 have very much proved Yang right. While the party’s over, his passing provides a good opportunity to recall what a fine time it was.
From a blog I write: 12 November 2020 https://luysii.wordpress.com/2020/11/12/math-can-be-hard-even-for-very-smart-people/
Math can be hard even for very smart people
50 McCosh Hall in Princeton, an autumn evening in 1956. The place was packed. Chen Ning Yang was speaking about parity violation. Most of the people there had little idea (including me) of what he did, but wanted to be eyewitnesses to history. . . But we knew that what he did was important and likely to win him the Nobel (which happened the following year).
That’s not why Yang is remembered today (even though he’s apparently still alive at 98). Before that he and Robert Mills were trying to generalize Maxwell’s equations of electromagnetism so they would work in quantum mechanics and particle physics. Eventually this led Yang and Mills to develop the theory of nonAbelian gauge fields which pervade physics today.
Yang and James Simons (later the founder of Renaissance technologies and already a world class mathematician — Chern Simons theory) later wound up at Stony Brook. Simons told him that gauge theory must be related to connections on fiber bundles and pointed him to Steenrod’s The Topology of Fibre Bundles. So he tried to read it and “learned nothing. The language of modern mathematics is too cold and abstract for a physicist.”
Another Yang quote “There are only two kinds of math books: Those you cannot read beyond the first sentence, and those you cannot read beyond the first page.”
So here we have a brilliant man who invented significant mathematics (gauge theory) along with Mills, unable to understand a math book written about the exact same subject (connections on fiber bundles).
Wonderful account of his contributions to particle physics. However, he (and TD Lee) also contributed to statistical mechanics. His name also lives on in mathematical physics, in Yang-Baxter equation, and derivatives like “Yangian,”
liuyao,
Thanks! What I wrote was certainly not intended to be a comprehensive account of Yang’s contributions to physics, just the high points of the ones that I understand pretty well.
It is little wonder that Yang, assisted by Mills, gave birth to the Yang–Mills theory.
He wove together the threads of two great legacies—
the subtle geometry he absorbed from S. S. Chern in war-time Kunming,
and disciplined particle physics he learned from Enrico Fermi in post-war Chicago.
And likewise, it is no mystery that Bohr forged his early quantum model:
he blended the precision of British experimental craft,
learnt under Rutherford and Thomson,
with the depth of German theoretical insight,
shaped by Planck and Einstein.
Each stood at a crossroads of cultures and minds—
and from such crossings, new worlds are born.
Really hard to imagine how Wu didn’t win the Nobel Prize too.
liuyao,
Right. I knew Lee and Yang from the Lee-Yang theory of phase transitions well before I learned about their, much more famous, contributions to particle physics.
Lee and Yang were unusual in that they made their big breakthroughs while affiliated with Princeton’s IAS, as opposed to being appointed there after already becoming famous.
A true giant and conscience of high-energy particle physics and gauge-field theory who also made important contributions to statistical physics. I am sad to learn about his passing. He has a secured place in my heart. Rest In Peace, Frank!
Chen-Ning Yang wrote: «Have the great achievements of high-energy physics over the past seventy years brought any real benefits to human life? No». Too bad that other collider physicists pretend otherwise.
The Wu of the “Wu-Yang dictionary” is Tai Tsun Wu not Chien Shiung Wu.
«Have the great achievements of high-energy physics over the past seventy years brought any real benefits to human life? No»
This again? Is short term human benefit the metric we are judging all our works by? Should we also recall the James Webb telescope then? Or is there a carve-out for astronomy for “ancient human longing for the heavens” and whatnot?
Alessandro Strumia/Amitabh Lath,
I think it’s legitimate to point to Yang’s late in life skeptical remarks about colliders, but it’s important to remember that the context was the ongoing discussion in China about a specific proposal. This particular quote seems to me, like the one in the comment above about math books, Yang trying to be provocative, and not in an interesting way. The math book quote also has some context (Simons telling Yang to read Steenrod, a really bad idea). So, please resist the provocations to start up a general defense of either the value of colliders or of math books.
https://www.youtube.com/watch?v=JZqwP7b2kJY
Chen-Ning Yang: Paper with Mills on Gauge theories
Simons Foundation: has interesting short interviews with Chen-Ning Yang.
Dave,
https://physicsworld.com/a/credit-where-credits-due/ gives some interesting background for the Nobel controversy surrounding Wu.
I have exactly the same difficulties when it comes to graduate math texts. It is a source of endless frustration, but the Bourbaki/axiomatic approach that is apparently so natural for creating new mathematics is very foreign to physics training, where mathematical tools are acquired in the course of solving physics problems.
This is why lecture notes or textbooks that attempt to translate modern mathematical results into physicists’ language (what is it, how do I use it) are so crucial and yet are often critically undervalued.
Matthew Foster,
The Bourbaki style exposition in textbooks has long ago fallen out of favor among mathematicians. It’s not very good for learning a subject, quite useful if you already know a subject and are looking for precise definitions and statements about the subject that you can use for other purposes.
You can these days find much more readable expositions of lots of modern mathematics, There’s still a huge language problem and problem of motivation. Higher level mathematics is generally written assuming a background few physicists have. Also, the motivation is typically to develop a theory covering a very wide class of examples, while physicists are typically interested in a specific example.
There’s a lot more of interest to discuss about the communication problems between mathematicians and physicists, but better that be left for another time.
Could you please give some advice on how to study Yang-Mills theory? For someone, say relatively comfortable with your Quantum and Representation book. Perhaps separate pathways for math and physics leaning minds? Are you going to add more about this in the revision of your book? Thanks.
ZG,
In the quantum book I try and do (chapter 45) the U(1) gauge theory (photons) from a point of view that generalizes to the non-abelian (Yang-Mills) case. There’s a very short section (45.5) about Yang-Mills.
I’ve always wanted to write another book, about geometry for physicists, have never gotten to that. I first learned a lot about this from the Eguch/Gilkey/Hanson Physics Reports article, but would be interested to hear from others of good more recent sources.
Eguchi, T., Gilkey, P. B., & Hanson, A. J. (1980). Gravitation, gauge theories and differential geometry. Physics reports, 66, 213-393.
But this is about classical Yang-Mills theory only, not the quantum field theory of interest in physics. For the latter (from a mathematical physics perspective) see, e.g.,
Hollands, S. (2008). Renormalized quantum Yang–Mills fields in curved spacetime. Reviews in Mathematical Physics, 20, 1033-1172.
https://arxiv.org/abs/0705.3340
For the Yang-Mills Millennium problem, see
Jaffe, A., & Witten, E. (2006). Quantum yang-mills theory. The millennium prize problems, 1, 129.
For the (exactly solvable) case in 2-dimensional spacetime, see, e.g.,
Blau, M., & Thompson, G. (1992). Quantum Yang-Mills theory on arbitrary surfaces. International Journal of Modern Physics A, 7(16), 3781-3806.