Gravity and Spin Forces in Gravitational Quantum Field Theory**Supported in part by the National Science Foundation of China (NSFC) under Grant Nos. 11690022 and 11475237, Strategic Priority Research Program of the Chinese Academy of Sciences (CAS), under Grant No. XDB23030100, Key Research Program QYZDYSSW-SYS007, and the CAS Center for Excellence in Particle Physics (CCEPP)

Abstract

In the new framework of gravitational quantum field theory (GQFT) with spin and scaling gauge invariance developed in Phys. Rev. D 93 (2016) 024012-1, 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 Newtonʼs gravitational law in the early universe is modified due to the background field. The spin dependence of the gravitational potential is demonstrated.