Gupta-Feynman based Quantum Field Theory of Einstein's Gravity

M. C. ROCCA; A. PLASTINO

JOURNAL OF PHYSICS COMMUNICATIONS

IOP PUBLISHING LTD

Lugar: LONDRES; Año: 2020 vol. 4 p. 35014 - 35024

2399-6528

This paper is an {sf application} to Einstein´s gravity (EG) of themathematics developed in A. Plastino, M. C. Rocca:J. Phys. Commun. {f 2}, 115029 (2018). We will quantize EG by appeal to the most general quantization approach, the Schwinger-Feynman variational principle, which is more appropriate and rigorous that the functional integral method,when we are in the presence of derivative couplingsd We base our efforts on works by Suraj N. Gupta and Richard P. Feynman so as toundertake the construction of a Quantum Field Theory (QFT) ofEinstein Gravity (EG). We explicitly use the Einstein Lagrangian elaboratedby Gupta cite{g1} but choose a new constraint for the theorythat differs from Gupta´s one. In this way, we avoid the problem of lack of unitarity for the $S$ matrix that afflicts the procedures ofGupta and Feynman.Simultaneously, we significantly simplify the handling of constraints. This eliminates the need to appeal to ghosts for guarantying the unitarityof the theory.Our ensuing approach is obviously non-renormalizable. However, this inconvenience can be overcome by appealing tho the mathematical theorydeveloped by Bollini et al. cite{tp3,tp18,tp19,tp20,pr}Such developments were founded in the works of Alexander Grothendieck cite{gro}and in the theory of Ultradistributions of Jose Sebastiao e Silva cite{tp6}(also known as Ultrahyperfunctions).Based on these works, we have constructed a mathematicaledifice, in a lapse of about 25 years, that is able to quantize non-renormalizable Field Theories (FT).Here we specialize this mathematical theory to treat the quantum field theory of Einsteins´s gravity (EG). Because we are using a Gupta-Feynman inspired EG Lagrangian, we areable to evade the intricacies of Yang-Mills theories.