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

[1]	Plastino, A. and Rocca, M.C. (2018) Quantum Field Theory, Feynman-, Wheeler Propagators, Dimensional Regularization in Configuration Space and Convolution of Lorentz Invariant Tem pered Distributions. Journal of Physics Communications, 2, Ar ticle ID: 115029. [CrossRef]
[2]	Bollini, C.G., Escobar, T. and Rocca, M.C. (1999) Convolution of Ultradistributions and Field Theory. International Journal of Theoretical Physics, 38, 2315-2332. [CrossRef]
[3]	Bollini, C.G. and Rocca, M.C. (2004) Convolution of Lorentz In variant Ultradistributions and Field Theory. International Jour nal of Theoretical Physics, 43, 1019-1051. [CrossRef]
[4]	Bollini, C.G. and Rocca, M.C. (2004) Convolution of n Dimensional Tempered Ultradistributions and Field Theory. In ternational Journal of Theoretical Physics, 43, 59-76. [CrossRef]
[5]	Bollini, C.G., Marchiano, P. and Rocca, M.C. (2007) Convolution of Ultradistributions, Field Theory, Lorentz Invariance and Res onances. International Journal of Theoretical Physics, 46, 3030-3059. [CrossRef]
[6]	Plastino, A. and Rocca, M.C. (2020) Non-Relativistic Quantum Field Theory of Verlindes Emergent Entropic Gravity. Annals of Physics, 412, Article ID: 168013. [CrossRef]
[7]	Sebastiao e Silva, J. (1958) Les fonctions analytiques comme ultra-distributions dans le calcul oprationnel. Mathematische An nalen, 136, 38-96. [CrossRef]
[8]	Schwartz, L. (1966) Th′eorie des distributions. Hermann, Paris.
[9]	Bollini, C.G. and Giambiagi, J.J. (1972) Lowest Order “Diver gent” Graphs in v-Dimensional Space. Physics Letters B, 40, 566-568. [CrossRef]
[10]	Bollini, C.G. and Giambiagi, J.J. (1972) Dimensional Renorinal ization: The Number of Dimensions as a Regularizing Parameter. Il Nuovo Cimento B, 12, 20-26.
[11]	Bollini, C.G. and Giambiagi, J.J. (1996) Dimensional Regulariza tion in Configuration Space. Physical Review D, 53, 5761. [CrossRef]
[12]	Plastino, A. and Rocca, M.C. (2020) Gupta-Feynman based Quantum Field Theory of Einstein’s Gravity. Journal of Physics Communications, 4, Article ID: 035014. [CrossRef]
[13]	Plastino, A. and Rocca, M.C. (2020) Quantization of Newtons Gravity. Journal of Modern Physics, 11, 920-927. [CrossRef]
[14]	Zamora, D.J., Rocca, M.C., Plastino, A. and Ferri, G.L. (2018) Dimensionally Regularized Boltzmann-Gibbs Statistical Mechan ics and Two-Body Newtons Gravitation. Physica A: Statistical Mechanics and Its Applications, 503, 793-799. [CrossRef]
[15]	Zamora, D.J., Rocca, M.C., Plastino, A. and Ferri, G.L. (2018) Dimensionally Regularized Tsallis Statistical Mechanics and Two-Body Newtons Gravitation. Physica A: Statistical Mechan ics and Its Applications, 497, 310-318. [CrossRef]
[16]	Gel’fand, I.M. and Shilov, G.E. (1964) Generalized Functions, Vol. 1. Academic Press, Cambridge, MA.
[17]	Gradshteyn, I.S. and Ryzhik, I.M. (1980) Table of Integrals, Se ries and Products. Academic Press, Cambridge, MA.