Interesting QFT Problems Tackled in New Fashion - Plastino, Ángel Luis (2020)
The Dimensional Regularization technique of Bollini and Giambiagi (BG) [Phys. Lett. B 40, 566 (1972); Il Nuovo Cim. B 12, 20 (1972); Phys. Rev. D 53, 5761 (1996)] cannot be employed for all Schwartz Tempered Distributions Explicitly Lorentz Invariant (STDELI) S′ L. We lifted such limitation in [J. Phys. Comm. 2 115029 (2018)], which opens new QFT possibilities, centering in the use of STDELI that allows one to obtain a product in a ring with zero divisors. This in turn, overcomes all problems regrading QFT in nities. We provide here three examples of the application of our STDELI-extension to quantum eld theory (A) the exact evaluation of an electron's self energy to one loop, (B) the exact evaluation of QED's vacuum polarization, and C) the λϕ4 4! theory for six dimensions, that is non-renormalizable.