Interesting QFT problems tackled in new fashion

A. PLASTINO; M. C. ROCCA

JOURNAL OF HIGH ENERGY PHYSICS, GRAVITATION ADN COSMOLOGY

SCIENTIFIC RESEARCH PUBLISHER

Lugar: Hong Kong; Año: 2020 vol. 6 p. 590 - 608

2380-4327

The Dimensional Regularization technique of Bollini and Giambiagi (BG) [Phys. Lett. {f B 40}, 566 (1972); Il Nuovo Cim. {f B 12}, 20 (1972); Phys. Rev. {f D 53}, 5761 (1996)]can not be employed for {it all} Schwartz Tempered DistributionsExplicitly Lorentz Invariant (STDELI) ${cal S}^{´}_L$. We lifted such limitation in [J. Phys. Comm. {f 2} 115029 (2018)]. The ensuing generalization to allSTDELI allows one to obtain a product in a ringwith zero divisors. Using the inverse Fouriertransform (IFT) we get the ring with zero divisors ${cal S}^{´}_{LA}$,defined as ${cal S}^{´}_{LA}={cal F}^{-1}{{cal S}^{´}_L}$,where ${cal F}^{-1}$ denotes the IFT. Inthis manner we effect (i) a dimensional regularization in momentumspace (the ring ${cal S}^{´}_{L}$) via convolution, and (ii) a productof distributions in the corresponding configuration space (thering ${cal S}^{´}_{LA})$. This generalizes the results obtainedby BG for Euclidean space in [Phys. Rev. {fD 53}, 5761 (1996)].We provide here two examples of the application of our STDELI-extension toquantum field theory (A) the exact evaluation of an electron´s self energy to one loopand (B) the exact evaluation of QED´s vacuum polarization.