Structural identities in the first order formulation of quantum gravity

TL;DR

This paper investigates the consistency conditions of the first order quantum gravity formulation, deriving structural identities that relate Green's functions involving auxiliary fields to those with classical graviton fields, ensuring formal self-consistency.

Contribution

It introduces a set of structural identities specific to the first order quantum gravity formalism, distinct from Ward identities, crucial for its self-consistency.

Findings

Derived structural identities linking auxiliary and graviton Green's functions.

Provided a simple interpretation of the auxiliary quantum field.

Ensured the self-consistency of the first order quantum gravity approach.

Abstract

We study the self-consistency of the first order formulation of quantum gravity, which may be attained by introducing, apart from the graviton field, another auxiliary quantum field. By comparing the forms of the generating functional $Z$ before and after integrating out the additional field, we derive a set of structural identities which must be satisfied by the Green's functions at all orders. These are distinct from the usual Ward identities, being necessary for the self-consistency of the first order formalism. They relate the Green's functions involving the additional quantum field to those containing a certain composite graviton field, which corresponds to its classical value. Thereby, the structural identities lead to a simple interpretation of the auxiliary field.