Tuesday, June 16, 2020

Homework from Feynman (1997-1998): formulate string theory

Beauty: Robbert Dijkgraaf, the director of IAS Princeton and once a co-author of misogynist homophobic capitalist racists, wrote a wonderful Quanta Magazine essay about the two types of beauty in mathematics, generic and exceptional. The exceptional taste of beauty seems more generic ;-) among scientists but the generic sense of beauty is ultimately needed, too. Kepler was obsessed with the exceptional beauty (Platonic polyhedra) before he discovered the wagon of manure (ellipses) that gave rise to the Newtonian quantatitative revolution in physics.

Warlords from "Black Lives Matter" and "Antifa" (whose new "constructive" slogan is shut down STEM, so kind!) generously allowed new papers to appear on arXiv.org today. Thanks a lot for your mercy, comrades. The last hep-ph "paper" has 98 pages and 117 figures:
Feynman Lectures on the Strong Interactions
You may know one of the authors, Richard Feynman. The other one – who is probably responsible for the submission (assuming the resurrection no-go theorem) – is James Cline. Feynman died after an acute cancer episode on February 15th, 1988. But these 22 lectures were supposed to be a full course at the Caltech Grad School (1987-1988) and the plan was to turn this course into a booklet, too.

I think that Feynman's lectures on QCD are fun – and more playful than the typical dry QCD course. So Feynman does talk about the gauge symmetry, the Lagrangian and the Hamiltonian of QCD, renormalization, various diagrams. But the father of "partons" also talked about various approximate ways to look at the bound states of quarks and gluons, among other things. Some of the explanations may be viewed as graduate school continuations of the examples of quantum mechanics in the Feynman Lectures on Physics (think about the kaons' oscillations over there).

I was pretty sure that the lectures would mention the word "string" because string theory was still going through the First Superstring Revolution around 1987. And I was right. But the reality has exceeded my expectations. The word "string" appears 29 times in the PDF file. And the sentences aren't your typical sociological conspiracy theories by the average SJW crackpots like
string theory is a symbol of the white oppression and female colorful geniuses have to be placed on the same level as string theorists.
Instead, all Feynman's references to string theory are very technical and constructive. In Lecture 2 of 22, he discusses "other phenomenological models" and the old string theory is unsurprisingly the first one:
The first is the relativistic string, which was inspired by the observed Regge trajectories. These are plots of the spin versus mass squared...
Two figures show the Regge trajectories and baryons as quarks connected by the old string. In Lecture 3, he correctly mentions that the breakup of this string is really physically connected to the electron-positron production in the electric field (the difference is that the string, a flux tube, wants to be rather compact or thin because of the self-interactions, unlike the electric fields that spread in all directions and whose equations are linear). As you know, Feynman wouldn't name things after humans (let alone his fellow Nobel prize winners) so the words "Schwinger effect" simply couldn't appear there. ;-) But Feynman did praise Schwinger for his formulation of QFT whose parts Feynman had "stolen".

The Lecture 3 and its treatment of strings escalates, there are some Feynman diagrams with the world sheet in them – the usual 't Hooft's interpretation of the planar diagrams etc. which was refreshed after the late 1997 advances by Juan Maldacena. The word "string" appears a dozen of times before Feynman gets to the punch line:
Problem. What happens for the relativistic treatment of the string? We must formulate a relativistic equation. String theory!8. [Footnote 8: This was around the time of the first string revolution. I reproduce the following answer from RPF’s private notes.]
And indeed, the solution to the problem follows. Feynman writes the usual (string theory textbooks) integrals (multiplied by the string tension $$T$$) that describe the energy as well as the angular momentum of a string. The energy is the Hamiltonian and string theorists can't miss it. However, the formula for the angular momentum – and Feynman's proof of the Regge relationship – is already slightly non-standard. I want to say that it's very likely that Feynman understood some of the basic "mechanical properties of the relativistic string" more intimately than a not so negligible fraction of the actual string theorists – although these are really correct formulae.

In Lecture 4, Feynman dreams about some nice derivation of a phenomenological Hamiltonian (with the linear confining "string" potential). In Lecture 10, it is the "Dirac string" that Feynman was explaining but he returns to the stringy string in Lecture 13 and the Appendix A. I assure you that there's much more fun in the PDF file than the sentences containing the word "string" LOL.

But I obviously focused on Feynman's references to strings and string theory because Feynman is often quoted as an "authority" allegedly proving that string theory shouldn't be studied. Needless to say, it is complete rubbish. Feynman didn't understand the reasons why string theory was really a unique consistent theory of quantum gravity (and he just never mastered advanced and medium advanced topics of string theory, starting with the critical dimension!) but he still understood a lot – about the naturalness of the stringy equations and their application within the physics of hadrons. Even though 1987 was arguably the "year of the most enthusiastic pro-string hype ever" (that's when I read my first popular article about strings which got to my favorite journal, VTM, because Ondřej Neff slept with some female science journalist – I apologize to Neff if I distorted his story a little bit), Feynman didn't emit a single sentence that would resemble the contemporary SJW crackpots' bitterness about modern theoretical physics (and stupid Barbie's complaints about her getting lost in the math class).

Every good theoretical high-energy physicist has simply needed to dedicate a nonzero fraction of time to the ideas of string theory in recent 35 or 55 years and even in the last year of his life, Richard Feynman was no exception. The ideas of doing fundamental physics without strings are about as nutty as the ideas to abolish police.