Interesting QFT Problems Tackled in New Fashion

A. Plastino^1,2,3, M. C. Rocca^1,2,4

¹Departamento de Física, Universidad Nacional de La Plata, La Plata, Argentine.
²IFLP-Consejo Nacional de Investigaciones Cientìficas y Tecnoló gicas (IFLP-CCT-CONICET)-C. C., La Plata, Argentina.
³SThAR-EPFL, Lausanne, Switzerland.
⁴Departamento de Matem′atica, Universidad Nacional de La Plata, La Plata, Argentine.

DOI: 10.4236/jhepgc.2020.64040                

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.

Keywords

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

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

References

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