physics, mathematical physics, philosophy of physics
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Types of quantum field thories
The origins of perturbative quantum field theory go back to ideas on quantum electrodynamics due to Julian Schwinger, Shin'ichirō Tomonaga, Richard Feynman, Freeman Dyson.
While highly succesful, the conceptual nature of the original formulation, in particular of the process of renormalization (“removal of UV-divergences”), had remained mysterious. In Feynman 85, Chap. 4. “Loose Ends” it still says:
…is technically called ‘renormalization.’ But no matter how clever the word, it is what I would call a dippy process! Having to resort to such hocus-pocus has prevented us from proving that the theory $[...]$ is self-consistent. It’s surprising that the theory still hasn’t been proved self-consistent one way or the other by now; $[...]$ What is certain is that we do not have a good mathematical way to describe the theory of quantum electrodynamics: such a bunch of words… (Feynman 85, Chap. 4. “Loose Ends”)
These conceptial mysteries were later resolved in a mathematically rigorous formulation of renormalization in perturbative quantum field theory on Minkowski spacetime by (Epstein-Glaser 73), based on (Bogoliubov-Shirkov 59 and Stückelberg 51), now known as causal perturbation theory and perturbative algebraic quantum field theory; laid out, together with other rigorous approaches, in the seminal Erice summer school proceedings (Velo-Wightman 76).
Richard Feynman, QED: The Strange Theory of Light and Matter, 1985
Silvan Schweber, QED and the men who made it: Dyson, Feynman Schwinger and Tomonaga, Princeton Series in Physics, 1994