Feynman diagrams representing the interactions of subatomic particles were introduced by Richard Feynman in 1948. The first published Feynman diagram appeared in Physical Review in 1949.
Did Feynman diagrams play a key role in the creation of the electroweak theory developed between 1949 and 1967 in the work of Yang and Mills, Glashow, Higgs, Weinberg, Salem and their collaborators?
If so, please explain how (for instance these diagrams might have rendered some difficult calculations more feasible).
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$\begingroup$ They played a key role in establishing the significance of renormalizability for theories generally. The electroweak theory took shape after its renormalizability was assured by the Higgs mechanism. $\endgroup$– ConifoldNov 10, 2020 at 20:35
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1$\begingroup$ See e.g. Kibble, History of electroweak symmetry breaking:"But in all these models, the symmetry breaking, giving the W and Z bosons masses, had to be inserted by hand, and theories of spin-1 bosons with explicit masses were well known to be non-renormalizable and thus unphysical. The big question therefore was: could this be a case of spontaneous symmetry breaking?" $\endgroup$– ConifoldNov 10, 2020 at 20:46
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$\begingroup$ Do you mean they played a key role for proving the renormalizability property for theories (including electroweak theory?) or do you mean something else by "the significance of renormalizability"? $\endgroup$– Ansonī BōdoNov 11, 2020 at 9:32
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1$\begingroup$ They played a key role already in making sense of what the renormalizability is. It is what gets you finite values of diagram amplitudes after making the high energy cutoff and inserting the measured values of masses and charges by hand. Crafting the very structure of the theory was guided by the renormalizability constraint, see The conceptual foundations and the philosophical aspects of renormalization theory for a historical analysis. $\endgroup$– ConifoldNov 12, 2020 at 0:38
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1$\begingroup$ "As Weinberg (1980a) remarked in his Nobel lecture, if he had not been guided by the principle of renormalizability, his theory of electroweak interactions would have received contributions not only from $SU (2) \times U (1)$-invariant vector boson exchanges - which were believed to be renormalizable... - but also from $SU(2)\times U(1)$-invariant four-fermion couplings, which were known to be nonrenormalizable, and the theory would have lost most of its predictive power." $\endgroup$– ConifoldNov 12, 2020 at 0:41
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Julian Schwinger said of Feynman diagrams:
that they brought QFT to the masses.
However, he along with Sin-Itiro Tomonaga independently developed an alternative formalism that is non-perturbative from the beginning, in contrast to Feynmans perturbative approach.
Feynmans approach, being perturbative, misses a great deal. One does not need to know QFT to see this.
After all, the functions that are perturbative on the real line are exactly the analytic functions. But these are subsumed by the smooth functions. That is there are many more smooth functions than there are analytic ones. And this is before one begins to examine the possibility that non-smooth functions also play a role - as they do with say, Diracs delta function and their derivatives.
More physically speaking, instantons are twists in vector bundles, and are global phenomena. And being global they are missed by physics which only probe locally, as Feynman diagrams do.
