Approximate reformulation a recent non-renormalizable QFT's methodology and Einstein's Gravity

M. C. ROCCA; A. PLASTINO

JOURNAL OF HIGH ENERGY PHYSICS, GRAVITATION AND COSMOLOGY

SCIENTIFIC RESEARCH PUBLISHING

Año: 2020 vol. 6 p. 298 - 311

2380-4327

We revisit, advancing a useful approximation, a recently formulated QFT treatment that successfully overcomes any troubles with infinities for non-renormalizable QFTs [J. Phys. Comm. {f 2} 115029 (2018)]. Such methodology was able to successfully deal, in non-relativistic fashion, with Newton´s gravitation potential [Annals of Physics {f 412}, 168013 (2020)]. Our present approximation to the QFT method of [J. Phys. Comm. {f 2} 115029 (2018)] is based on the Einstein´s Lagrangian (EG) elaboratedby Gupta cite{g1}, save for a different constraint´s selection. This choice allows one to avoid the lack of unitarity for the $S$ matrix that impaired the proceedings ofGupta and Feynman. Moreover, we are able to simplify the handling of such constraint by eliminating the need to involve ghosts for guarantying unitarity. {it Our approximation consists in setting the graviton field $phi^{mu u} = gamma^{mu u}phi$,where $gamma^{mu u}$ is a constant tensor and $phi$ a scalar (graviton) field}.The ensuing approximate approach is non-renormalizable, an inconvenience that we are able to overcome in [J. Phys. Comm. {f 2} 115029 (2018)].