Integral representations for matter fields with electromagnetic interaction in quantum Einstein gravity

R Yoshida

doi:10.1093/ptep/ptu133

Abstract

Integral representations for the electromagnetic field and the electron one are presented in the manifestly covariant operator formalism of quantum gravity. These representations contain not only the gravitational interaction but also the electromagnetic one, and satisfy the matter field equations. Some properties of them are investigated.

Highlights

In 1992, Abe and Nakanishi [1] proposed a method for solving the manifestly covariant operator formalism of quantum electrodynamics
We show that the gravitational BRST transformation of S(x, y; m) is given by
Using (2.41), (2.42), (2.45), (3.42), (3.45), (4.48), and (4.49), we find that the integral representation (4.19) for Aμ is invariant under the internal Lorentz BRST transformation

Summary

Introduction

In 1992, Abe and Nakanishi [1] proposed a method for solving the manifestly covariant operator formalism of quantum electrodynamics. The purpose of the present paper is to give integral representations for the electromagnetic field and the electron one in quantum gravi-electrodynamics, and to investigate their properties. For this purpose, we use the quantum-gravity Pauli–Jordan D function [5,6] and a tensorial q-number commutator function [7] for the electromagnetic field, and introduce a quantum-gravity version of the S function for the electron one. 4, we propose integral representations for the electromagnetic field and the electron one, using the quantum-gravity Pauli–Jordan D function, the tensorial q-number commutator function, and the quantum-gravity S function; we show the transformation properties of these representations.

Covariant operator formalism of quantum gravi-electrodynamics

Transformation properties

Discussion