Gravity and Spin Forces in Gravitational Quantum Field Theory

TL;DR

This paper develops a perturbative quantum field theory framework for gravity incorporating spin and scaling gauge invariance, analyzing early universe inflation, and deriving modified gravitational interactions with spin effects.

Contribution

It introduces a new gravitational quantum field theory with gauge invariance, decomposes fields into SO(3) representations, and calculates scattering amplitudes including spin-dependent gravitational potentials.

Findings

Modified Newtonian potential in early universe background

Demonstration of spin dependence in gravitational interactions

Derivation of propagators and Feynman rules for quantum gravity fields

Abstract

In the new framework of gravitational quantum field theory (GQFT) with spin and scaling gauge invariance developed in Phys. Rev. D\textbf{93} (2016) 024012-1~\cite{Wu:2015wwa}, we make a perturbative expansion for the full action in a background field which accounts for the early inflationary universe. We decompose the bicovariant vector fields of gravifield and spin gauge field with Lorentz and spin symmetries SO(1,3) and SP(1,3) in biframe spacetime into SO(3) representations for deriving the propagators of the basic quantum fields and extract their interaction terms. The leading order Feynman rules are presented. A tree-level 2 to 2 scattering amplitude of the Dirac fermions, through a gravifield and a spin gauge field, is calculated and compared to the Born approximation of the potential. It is shown that the Newton's gravitational law in the early universe is modified due to the background field. The spin dependence of the gravitational potential is demonstrated.