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

Abstract

This paper is an application to Einstein's gravity (EG) of the mathematics developed in (Plastino and Rocca 2018 J. Phys. Commun. 2, 115029). 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 couplingsWe base our efforts on works by Suraj N. Gupta and Richard P. Feynman so as to undertake the construction of a Quantum Field Theory (QFT) of Einstein Gravity (EG). We explicitly use the Einstein Lagrangian elaborated by Gupta (Gupta, Proc. Pys. Soc. A, 65, 161) but choose a new constraint for the theory that differs from Gupta's one. In this way, we avoid the problem of lack of unitarity for the S matrix that afflicts the procedures of Gupta and Feynman. Simultaneously, we significantly simplify the handling of constraints. This eliminates the need to appeal to ghosts for guarantying the unitarity of the theory. Our ensuing approach is obviously non-renormalizable. However, this inconvenience can be overcome by appealing tho the mathematical theory developed by (Bollini et al Int.

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“…Previous attempts to quantize Einstein gravity (EG) have failed because of 1) they utilize a Rigged Hilber Space (RHS) with undefined metric, 2) non-unitarity troubles, and 3) non-renormalizablity problems. These problems were successfully bypassed in [1] [2], yielding a viable quantification procedure for Einstein's gravity. One used two kinds of tools.…”