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I do not agree with the statement, that the lack of mathematical rigor is a major reason for not teaching the path integral formalism in quantum mechanics. The common physicist is normally not interested in complete mathematical rigor, as long as the concepts make sense from a physical point of view and produce the right results. A good example of this is ...


7

I would like to add a slightly more technical answer to supplement the other (although it is a bit late). It may be helpful, I think, and it touches a broader issue which interesting. It's a conflict of history of teaching versus history of the mathematical prerequisites for the material. First of all, supposing the topic material is taught early on, how ...


6

Let me try to summarize what was said in the comments and add something. (I am a teacher of mathematics, not physics, but this is close). First of all not all students study Lagrangian mechanics at an early stage. It requires much more mathematical sophistication than most undergraduate students have. (I am talking of US here). Second, Feynman's integral ...


5

The use of color to refer to the "color charge" characteristic of QCD is present in Gell-Mann, Fritzsch and Bardeen's original work from 1972. This terminology was apparently due to Gell-Mann: "They had actually begun exploring this possibility in their earlier paper at the Tel Aviv conference. Now, working with Bardeen, they elaborated on the idea. What ...


5

H.E. Stanley's 2002 interview has Harvard, taking quantum field theory ahead of quantum mechanics, Schwinger and a tough lecturer (Coleman), Wendell Furry, the electromagnetism course, and an exam. But the anecdotal details do not match up: Coleman discouraged him from going into QFT (he encouraged Jeff Mandula instead), the exam was take home, Furry was not ...


4

Comprehensive sources on the history of renormalization are Cao-Schweber survey paper and Cao's book. On the diagrams specifically the source Kaiser's Drawing Theories Apart: The Dispersion of Feynman Diagrams in Postwar Physics, see also his interview to American Scientist. According to Kaiser, one of the first published diagrams (reproduced below) appears ...


3

The Wikipedia coverage of the history is pretty spot on, and there is hardly a point in exactly dating the incremental formal developments of the second quantization picture of Dirac, Jordan, Wigner, Pauli, and Heisenberg, etc. QED has served since as a prototype of arbitrary creation and annihilation of matter and antimatter, made possible by relativity, ...


3

I think the quote (a reference would be good) is more about the OPE than the RG although they are very closely related and must have germinated in Wilson's mind concurrently. About Wilson's priority regarding the OPE, the correct date for his paper is 1964 rather than 1969 which seems to make his contribution posterior to that of the Soviet School. They didn'...


3

For quantum mechanics path integral can be done rigorously using Feynman-Kac formula and analytic continuation, but the approach is by no means elementary. A single look at the Feynman-Kac formula shows why it is not a great place for students to start at. Moreover, understanding where it comes from is itself a chore. While path integral heuristics are ...


2

This paper is an analysis of Feynman's early work with Feynman diagrams, and should help you find the answer. Also look at Freeman Dyson's early papers, where he explains Feynman's techniques.


2

The question is closely tied to the existence of "virtual particles", elusive intermediaries in particle collisions whose "paths" appear as wavy lines on Feynman diagrams. The current majority view of them seems to be as expressed e.g. on Strassler's blog, "the Feynman diagram is actually a calculational tool, not a picture of the physical phenomenon", see ...


1

@Oбжорoв answered this in the PSE: a source is Robert J. Sciamanda, Am. J. Phys. 81, 645 (2013); doi: 10.1119/1.4812316, By extending some of Hobson’s ideas, I arrive at the conclusion that in addition to there being no particles, there are not even fields!


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It's a long story, and students are constantly confused about the point even today. The basic appreciation that a quantized field is an infinite collection of quantum oscillators suitably organized is Pascual Jordan's, of course. But the technical innovations of 2nd quantization methods, the specific "packaging" of them is Dirac's. In some chronological ...


1

Original renormalization papers that came out in 1947-48 by Bethe, Lewis, Schwinger and Tomonaga did not use Feynman diagrams, not even Feynman's own 1948 paper did. Here is Cao-Schweber's description and comparison of their approaches: "Neither Lewis nor Schwinger nor Tomonaga made explicit use of a cutoff. They directly identified the divergent terms ...


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