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Gel’fand, I.M. and Shilov, G.E. (1964) Generalized Functions, Vol. 1. Academic Press, Cambridge, MA.

has been cited by the following article:

• TITLE: Interesting QFT Problems Tackled in New Fashion

  AUTHORS: A. Plastino, M. C. Rocca

  KEYWORDS: Dimensional Regularization Generalization, Electron Self Energy, Vacuum Polarization, Six-Dimensional Non Renormalizable λ(∅4/4!) Theory

  JOURNAL NAME: Journal of High Energy Physics, Gravitation and Cosmology, Vol.6 No.4, August 17, 2020

  ABSTRACT: 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 infinities. We provide here three examples of the application of our STDELI-extension to quantum field 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 theory for six dimensions, that is non-renormalizable.