Path Integral Quantization of Quantum Gauge General Relativity

TL;DR

This paper develops the path integral quantization framework for quantum gauge general relativity, deriving propagators, Feynman rules, and laying the groundwork for loop-level renormalization analysis.

Contribution

It provides the first detailed derivation of propagators, interaction vertices, and Feynman rules for quantum gauge general relativity within a path integral formalism.

Findings

Derived propagators for gravitational and ghost fields

Established Feynman rules for interaction vertices

Set the stage for loop-level renormalization calculations

Abstract

Path integral quantization of quantum gauge general relativity is discussed in this paper. First, we deduce the generating functional of green function with external fields. Based on this generating functional, the propagators of gravitational gauge field and related ghost field are deduced. Then, we calculate Feynman rules of various interaction vertices of three or four gravitational gauge fields and vertex between ghost field and gravitational gauge field. Results in this paper are the bases of calculating vacuum polarization of gravitational gauge field and vertex correction of gravitational couplings in one loop diagram level. As we have pointed out in previous paper, quantum gauge general relativity is perturbative renormalizable, and a formal proof on its renormalizability is also given in the previous paper. Next step, we will calculate one-loop and two-loop renormalization constant, and to prove that the theory is renormalizable in one-loop and two-loop level by direct calculations.