Saturday, May 22, 2021

Feynman Lectures on the Strong Interactions (Jim Cline notes)

Professor James Cline (McGill University) recently posted a set of lecture notes from Feynman's last Caltech course, on quantum chromodynamics. Cline, then a graduate student, was one of the course TAs and the notes were meant to be assembled into a monograph. Thanks to Tim Raben for pointing these out to me.

The content seems a bit more elementary than in John Preskill's Ph230abc, a special topics course on QCD taught in 1983-4. I still consider John's notes to be one of the best overviews of nonperturbative aspects of QCD, which is a rather deep subject. However as Cline remarks there is unsurprisingly something special about the lectures: Feynman was an inspiring teacher, presenting everything in an incisive and fascinating way, that obviously had his own mark on it.

The material on QFT in non-integer spacetime dimensions is, as far as I know, original to Feynman. Dimensional regularization of gauge theory was popularized by 't Hooft and Veltman, but the analytic continuation to d = 4 - ε is specifc to the loop integrals (i.e., concrete mathematical expressions) that appear in perturbation theory. Here Feynman is, more ambitiously, exploring whether the quantum gauge theory itself can be meaningfully extended to a non-integer number of spacetime dimensions. 
Feynman Lectures on the Strong Interactions  
Richard P. Feynman, James M. Cline 
These twenty-two lectures, with exercises, comprise the extent of what was meant to be a full-year graduate-level course on the strong interactions and QCD, given at Caltech in 1987-88. The course was cut short by the illness that led to Feynman's death. Several of the lectures were finalized in collaboration with Feynman for an anticipated monograph based on the course. The others, while retaining Feynman's idiosyncrasies, are revised similarly to those he was able to check. His distinctive approach and manner of presentation are manifest throughout. Near the end he suggests a novel, nonperturbative formulation of quantum field theory in D dimensions. Supplementary material is provided in appendices and ancillary files, including verbatim transcriptions of three lectures and the corresponding audiotaped recordings.
The image below is from some of Feynman's handwritten notes (in this case, about the Gribov ambiguity in Fadeev-Popov gauge fixing) that Cline included in the manuscript. There are also links to audio from some of the lectures. As in some earlier notebooks, Feynman sometimes writes "guage" instead of gauge.

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