My old friend and Princeton roommate Nathan Myhrvold has written an excellent piece about the anthropic principle and the Smolin-Susskind debate that has just been posted on the Edge web-site. It seems to me to summarize the issues very clearly.
After getting his Ph.D. in quantum gravity at Princeton, Nathan went to work as a post-doc with Stephen Hawking, and one of the topics he worked on involved a possible mechanism for explaining the small size of the cosmological constant. Nathan left physics and joined with some of my other friends from grad school days to start a software company near Berkeley that they called “Dynamical Systems”. They soon sold the company and themselves to Microsoft, where Nathan ended up in the position of Chief Technical Officer. He periodicaly reminds me that if I had taken up one of his many offers to come work with them back in the mid-eighties, I could be obscenely wealthy too. At the time I remember it seemed clear that it was much smarter to stay as a postdoc at Stony Brook, being paid enough to live on and able to think about whatever I wanted, than to go to California to work twenty hour days writing operating system code and getting paid in worthless pieces of paper.
Oh, well.
The formalism computes tree level amplitudes of gluon scattering in SYM very efficiently. No conformal invariance needed. These diagrams are the same as in the conformal theory.
For JC, the formalism reproduces the tree level amplitudes which is substantive in and of itself. Unfortunately, according to a followup by Berkovitz and Witten, it appears that the theory with loops will most likely reproduce the diagrams of conformal supergravity rather than those of N=4 SYM.
So, it seems likely at this point that the original proposal will not reproduce all of SYM, but, again, that doesn’t mean that there will be no future results on the subject. You can read Witten’s original big paper (the first half is all QFT — no string theory) for some intriguing facts about those loop amplitudes you referenced.
But, none of this changes the fact that the referenced paper is all about the very physical idea of doing scattering computations in Yang-Mills theory.
Aaron,
Do you know if anybody has been able to get Witten’s twistor formalism to work for the QCD 1-loop amplitudes and beyond?
If Witten’s twistor formalism has any substance in the end, it should be able to reproduce the 1-loop formulas found by Dixon, Kosower, & Bern during the 1990’s.
How pessimistic is it to think that something in its initial stages will never be extended to compute diagrams involving things other than gluons?
I am not claiming to be qualified to judge the details of this paper, but I would remind you that sooner or later conformal invariance must be broken as the world is quite obviously not conformally invariant. Penrose’s group worked for decades on ways of putting in masses and did not come up with anything very convincing. Maybe Witten’s team can do better, and I would be delighted if they could, but as things stand, this is a huge, and possibly insurmountable barrier.
“Thanks for that. Once again we see Witten et al, given a choice between physics and interesting math choosing the latter. ”
Interesting math? That paper gives new ways of doing computations in QCD. I consider that pretty damn physical. Don’t you think that’s at least somewhat interesting?
You can’t compute everything using this method, but I’m really astounded that you immediately dismiss it as ‘interesting math’. Did you read the paper?
And how pessimistic is it to think that something in its initial stages will never be extended to compute diagrams involving things other than gluons?
Your comment frankly couldn’t be more inapposite.
Danny, Chris, Steve
I remember years ago stories about some younger particle theory professors attempting to teach quantum field theory (QFT) courses in a “modern” context.
There were guys who started off with the path integral on the first day, and didn’t really mention much of the old canonical quantization way of doing things. By the end of the 1st semester, they were already finished covering numerous tree level calculations in phi^4, QED, and even some electroweak and/or QCD Standard Model stuff. Some folks even got as far as covering the renormalization of phi^4 theory or even QED in the 1st semester!
After about a month or so into the 1st semester, almost all of the experimentalists were scared off and subsequently stopped attending the lectures and/or dropped the course. By the time it was the 2nd semester of the course, the only folks left mostly consisted of theory students interested in particle physics and/or condensed matter. Mid way through the 2nd semester, many of the condensed matter folks disappeared too.
It seems like teaching QFT starting off with the path integral is almost like the equivalent of “culture shock” for many students.
Danny,
Thanks for that. Once again we see Witten et al, given a choice between physics and interesting math choosing the latter. Twistor space cannot deal with massive particles. This is unfortunate as not only is there clear experimental evidence for massive particles, but a lot of these masses have been measured to a high degree of precision. Maybe they can have massive particles as some kind of composite, but I am not aware of any developed theory that works on these lines. Maybe someone can prove me wrong – ?
Attn Chris – a paper you may find interesting:
http://xxx.lanl.gov/abs/hep-th/0403047
I like Weinberg QFT Vol. 1 a lot. I think that this is better than any other text book I have looked at. The later volumes I have not studied in detail, but one gets the impression that he is really trying to make sense of the material, and not just reproducing the results of other’s scientific papers. One also gets this sense from Bjorken and Drell – although these books can be annoying – but precious few others. Regarding Steve’s point about people not wanting to question Feynman-Dyson perturbation theory, I have the following comment: they question practically everything else! It seems however that this one thing is taboo. It is like a tower of Hanoi after ten turns – people fear that the tiniest disturbance in the air will cause the whole thing to collapse and they will no longer be able to talk about the “most accurate” or “best” theory of all time. Personally, I am not bothered as I never thought the tower existed anyway, except in people’s minds.
Weinberg is very odd as a writer. His book on gravity goes to great lengths to establish his heterodox opinion that “gravity is not geometry”, then he develops gravity as geometry in the most impeccable way. There is some of that in his QFT books.
I quite liked a book called “Quantum Field Theory of Point Particles and Strings” by B. Hatfield (some of it anyway). The last couple of chapters introduced perturbative string theory in a way that was much clearer to me than GSW vol 1. Ryder was also quite a good book and readable.
All QFT books are much of a muchness though and just present the usual sequence of stuff: free scaler, fermion, em fields, commutators, then Feynman-Dyson perturbation theory, S-matrix, phi^4 theory, QED, Feynman rules, vacuum polarisation etc. Then same results via path integrals, then renormalisation/regularisation. As a student, you never really get any clear or deep explanations in any text as to why you are even doing/learning this stuff in the first place.
I have never really enjoyed perturbation (it can also cause blindness:)or the whole Feynman-Dyson formalism. Quite tedious to learn. Amazingly, it works out though and lots of things can be computed to high accuracy in the end so students/authors don’t seem to question it or some of the underlying dodgy math. It is very entrenched in the theoretical physics culture so people like Chris who have chosen in the past to question aspects of it, won’t go down well with the establishment or journal editors. There is probably room for another QFT book if someone can put a new modern twist or approach on the subject with some vitality. Weinberg’s volumes were good but he is very much from the old school.
A big problem now though for the S-matrix formalism, and esp. for string theory, is you can’t actually define it on deSitter space, the space on which we appear to actually reside.
Dan Lunsford,
I skimmed the Jauch and Rohrlich book many years ago, but didn’t read it closely enough. On the surface it looked like it was written in a style and spirit similar to Heitler’s book.
In the intermediate zone of “advanced quantum mechanics” before quantum field theory (QFT), I really liked Paul Strange’s “Relativistic Quantum Mechanics: with Applications to Condensed Matter and Atomic Physics” book. It seems to cover many of the same sorts problems as undergraduate quantum mechanics, except done for the Klein-Gordan and Dirac equations. It attempts to explain intuitively what’s going on in various relativistic systems, which seems to be glossed over in most other “advanced quantum mechanics” books. Main thing I liked about Strange’s book was that it covered many relativistic quantum problems such as bound states for various potentials.
Most other “advanced QM” books seem to only really cover the Klein-Gordan & Dirac equations for various scattering processes and sometimes the hydrogen atom, with a view towards quantum field theory. For a long time I always felt that the study of bound states in relativistic quantum mechanics and/or quantum field theory, was generally neglected in favor of scattering processes.
JC – I’ve tried to answer this post 3 times, and I just don’t know. A lot of QFT is “overconceptualized” and one ends up with too many mantras. I’d frankly admit that it was a mess.
Did you ever see the book by Jauch and Rohrlich? (Theory of Photons and Electrons)
It’s remarkable that none of us can think of a totally acceptable text. This contrasts very strongly with GR, where one has any number of good texts, from all points of view.
BTW there is an intermediate zone, “Advanced Quantum Mechanics”, that is relatively neglected. There’s a bool by Schwabl I like. A good QFT book would I think build on that.
Danny,
If you wrote your own textbook on quantum field theory (QFT), what would you do to make the presentation better than other books like Ryder, Weinberg, Heitler, Kaku, etc …?
Originally I found the Ryder book the easiest to read when I was first learning QFT. Over the years I haven’t really found any QFT books that I really liked a lot. Though if I had to pick a book, it would be either Ramond’s field theory book or Veltman’s “Diagrammatica”.
This whole notion of using power series expansions in the free field grew out of my complete failure to get to grips with Feynman-Dyson perturbation theory. The more I tried to understand it, the less clear I was. This meant either one of two things: either (i) I was stupid or (ii) there was something wrong with it. It was not just conceit that made me decide on the latter: one thing about good scientific theories is that they are robust. Renormalization theory is not robust. If you take the limits in integrals in weird ways then you get weird answers. To say “well don’t take the limits in weird ways” is not acceptable. If it matters then the likelihood is that the limit does not exist and the whole thing is mathematically meaningless.
Anyway … the power series method is, under certain circumstances at least, consistent and comprehensible. Also I do not see why there should be a problem with the notion of an interacting field being a sum of tensor products of free fields – one can still see interactions taking place, and what is more, I do not see why the Wigner arguments about unitary irreducible irreps of the Poincare group should suddenly cease to be valid just because there are interactions. After all, all Wigner is doing is organising the vector space of a relativistic quantum mechanical system in a particular way and I see no reason why this should not be one that involves interactions. It is a bit like coupled oscillators in mechanics – just because one can pick out normal modes with their characteristic frequencies, etc. it does not mean that the individual oscillators that comprise the system have ceased to exist.
To answer the questions: (i) where it has gone – it is a structure that does not necessarily fall apart when one examines it carefully & is capable of generating scattering amplitudes that agree with tree Feynman graphs; (ii) where is is going – two-body bound states could be examined now; the anomalous magnetic moment of leptons could be calculated once it is clear how to represent the classical EM field … a number of things …
I suppose that if I had not been so easily discouraged I would have just hammered away at this regardless, but the fact was that I got very tired of being the only one saying these things and having programmed computers from the age of 11 it was easy to do this for a living and be thanked and paid properly for doing it. However this in no way means that I changed my mind about any of the physics issues. If anything the last 17 years of “fundamental” physics research has vindicated what I thought then. You cannot make a silk purse out of a sow’s ear, as they say.
Chris –
The 1986 paper is extremely interesting. Could you summarize your attitude at this moment about where this has gone, and could go? What most needs to be done?
-drl
Chris,
I wonder how much of the quantum field theory (QFT) framework as we know it today, is heavily biased from the Feynman perturbation theory picture. It seems like research into almost all other possible alternatives to QFT are largely ignored by the mainstream and/or are on the fringes of the physics community. (Only big exception would perhaps be string theory).
Do you know of any alternatives which does NOT use the “particle == field” correspondence, besides the string theory picture of particles corresponding to various string and/or brane excitations?
One of “promises” of string theory in the 1980’s that I really bought into at the time, was the idea that string theory could eventually explain the results obtained by renormalization in QFT. That “promise” seems to have fallen by the wayside over the years, where today not many string folks seem to like to talk about it.
With various stopgap measure like renormalization and path integrals, at times I wonder if we’re even looking at the correct degrees of freedom in QFT. Years ago I wondered why nobody has found an easy way to get quark bound states of mesons and baryons directly out of QCD, other than perhaps the lattice gauge theory folks running computer simulations and seeing the bound states. I felt that if there was a good direct QCD and/or electroweak derived model for hadrons, you should be able to easily see why the proton and neutron are relatively stable while the pi mesons, hadrons with strange quarks, etc … are all unstable, and where one could easily calculate their decay rates and bound state energies.
Danny,
No, you have not asked that before, so no apology required. My May 84 paper does not do much other than establish that you can expand an interacting quantum field in powers of the free field, and thereby calculate (interacting) matrix elements by inspection. One can do the same thing for any fields whose field equation has some characteristic coupling and which is such that the equations reduce to free field equations when this coupling goes to zero, so obviously it could be done for Yang-Mills as well. The nearest I have got to actually studying Yang-Mills in this framework was when I was looking at chiral fermions with a minimal coupling to a vector field; unfortunately I probably have not retained my notes (this was 1987) but I seem to remember finding that one had to have a vector self-coupling exactly on the lines of a Yang-Mills if one was to satisfy the requirement that fields (anti)commuted for spacelike intervals.
I am not working on it now, as (when I am not writing trading systems for banks) I am still trying to get basic stuff like the classical limit of a quantum field clear in my mind.
Chris –
Sorry if I asked this before, but can you do for any Yang-Mills field what you did for phi4 in the May ’84 paper? Are you working on that?
-drl
I’ve noticed over the years that many particle physics books (and even many review papers) seem to gloss over most of the QFT background, and frequently just goes straight into stating the Feynman rules and calculating Feynman diagrams. It seemed like the Feynman rules and Feynman diagram calculation prescriptions literally popped up out of thin air from nowhere, with very little to no theoretical justification on the surface (ie. just “take our word” for it, type of arguments).
Ahem, excuse me, but they might as well do this. The Feynman rules and renormalization prescription are all that they have. A connection with QFT is only possible if one permits the mathematically unpermissible, namely infinite subtractions.
The case against renormalization is argued at boring length on my web site (and will be argued at even more boring length when I have time to write the next installment), but let me add this snippet: there is no such thing as an infinite constant. If one has a divergent loop diagram then it is not acceptable to treat it as an “infinite constant” (to be cancelled by a counterterm) plus a finite functional part. Infinity plus an arbitrary function of any variables in the universe can be called infinity with no less justification. The “renormalized” amplitude can therefore have a functional dependency on variables that never even entered the original equations!
JC –
I think it would be hard to improve on a combination of Ryder, Weinberg, and Heitler, but there really isn’t an ideal single-volume treatment. I wish Ryder were fatter (more topics). I really love that book. As Chris suggests, Ryder places Wigner’s work in a prominent position.
I like the Kaku book as well, but it’s not a good textbook. I really think there is still room for a better textbook.
Chris,
Years ago I wondered about what it would take to write a book on quantum field theory (QFT) for undergrads. I was thinking of something along the lines of a QFT book which would be relatively “painless” to read, like the undergraduate particle physics book by David Griffiths. Of all the books I came across over the years on particle physics, the Griffiths one was the easiest to read and was relatively “painless” in comparison to most other books on particle physics.
I’ve noticed over the years that many particle physics books (and even many review papers) seem to gloss over most of the QFT background, and frequently just goes straight into stating the Feynman rules and calculating Feynman diagrams. It seemed like the Feynman rules and Feynman diagram calculation prescriptions literally popped up out of thin air from nowhere, with very little to no theoretical justification on the surface (ie. just “take our word” for it, type of arguments).
In QFT books which cover some particle physics, a lot of the really dense “difficult to understand” stuff seems to be largely justifying the perturbation theory prescriptions for doing the actual Feynman diagram calculations. I don’t know how it can be done offhand, but the challenge would perhaps be in coming up with a presentation which makes the dense “difficult to understand” machinery of QFT more transparent in an “easy to understand” language to a reader who only knows some undergraduate level quantum mechanics, electromagnetism, classical mechanics, and maybe statistical mechanics.
The simplest way I can think of offhand in presenting the “difficult to understand” machinery of QFT, would perhaps be looking at a single real scalar field theory with a phi^3 interaction as a simplified pedagogical example with the least amount of baggage to carry along.
I took a look at Heitler’s “quantum theory of radiation” book recently again, and noticed a lot of the classic quantum electrodynamics (QED) results were obtained from a first quantization framework, without really using QFT. It seemed like a messier formalism to do QED calculations, though Heitler did attempt to explain things in a more intuitive semi-classical picture than I’ve seen in modern QFT and particle physics books.
Hi JC,
The book would be a formal text whose thread would run somewhat like this:
1. Wigner unitary irreps of Poincare group, up to and including norms of vectors in these. Vectors in irreps as classical particles/fields. NB: First draft here (excluding classical limit arguments):
http://www.cgoakley.demon.co.uk/qft/RQM.pdf
2. Fock space as sums of tensor products of these vectors; Creation & annihilation operators defined from Fock space as per nice argument given in Weinberg Vol. 1 pp. 173-174; Identical particles and exchange symmetry; Quantum fields as 4D Fourier transforms of annihilation/creation ops; Spin-statistics theorem.
3. “Toy” interacting models with interacting field as sum of products of free fields in various configurations; calculation of scattering amplitudes using correspondence with time-dependent perturbation theory in ordinary QM.
4. Quantum Electrodynamics.
At this point I get a bit vague … I need to understand better how to get classical electrodynamics from the quantum one.
Er … that’s it so far. You understand that a lot of this is about providing a framework on which to build. This may well go in the direction of quasi- or non-local field equations to avoid infinities popping up. As you see, I have at no point formally quantized a classical field as I don’t believe that one needs to although I will do it for interest at some point.
Chris,
If you wrote a book about particle physics and/or physics in general, what would it be about?
The book you mention, “Nobel Dreams”, is by Gary Taubes (the mathematician Cliff Taubes’s brother). It was written during the mid-eighties and is quite entertaining. I read it a long time ago, and from what I remember it is very hard on Carlo Rubbia, to the extent of being pretty unfair. Rubbia is an overbearing guy, but he was the one who got the collider built at CERN that discovered the W and Z. Not at all clear that someone without his will-power could have done this.
I remember taking a class from Rubbia when I was an undergraduate. He was commuting back and forth to CERN and some days didn’t quite make it, but was quite a force of nature. I remember once when I was sitting in the second row I asked a question. He then pushed aside the seats in the front row to get to me, and gave me a vigorous answer right in my face. He really wanted to answer the question, but is was a bit of a scary experience.
Wasn’t there a book titled something like “Nobel Dreams …”, which discussed the dark side and politics of experimental particle physics research?
Hi Chris,
I should point out that I don’t have a tenured position at Columbia, although it is essentially a permanent one, which is the most important thing.
There’s a long on-going story about my attempts to write a book about some of these issues. I’ll tell this sometime when the situation is clearer about what is going to happen with that project.
Peter,
If the press were to ask me what I thought about string theory I would probably answer something on the lines of the following:
“I haven’t studied it, but I have trod in it.”
The problem is that my views carry very little weight. I could not get research posts after 1986 and have been out of the subject for over 17 years. They would probably just decide that my views were simply sour grapes. You, on the other hand, are a tenured professor at a prestigious university and as such, people do listen to what you have to say.
As for finances, maybe there might be some mileage in a popular science book arguing against the superstring collective insanity – ?
Even if it does not make you rich, it would make you feel better.
FWIW, I think you came out on top, money or no, to have avoided being tainted by Microsoft. Some things are more important than money (GASP).
A generation of people who sought to make an honest living at IT have suffered for those riches they enjoy.