Spin-2 gauge theories and perturbative gauge invariance

TL;DR

This paper investigates the gauge invariance of a massless self-interacting quantum tensor field, deriving conditions for gauge invariance and showing the most general coupling aligns with Einstein-Hilbert theory.

Contribution

It provides a field-theoretical derivation of gauge invariance conditions for spin-2 fields without relying on geometric assumptions from general relativity.

Findings

Gauge invariance conditions are derived at first order in perturbation theory.

The most general self-coupling matches that from Einstein-Hilbert action.

Gauge variation of the self-coupling is a divergence, ensuring gauge invariance.

Abstract

In the framework of causal perturbation theory we analyze the gauge structure of a massless self-interacting quantum tensor field. We look at this theory from a pure field theoretical point of view without assuming any geometrical aspect from general relativity. To first order in the perturbation expansion of the $S$-matrix we derive necessary and sufficient conditions for such a theory to be gauge invariant, by which we mean that the gauge variation of the self-coupling with respect to the gauge charge operator $Q$ is a divergence in the sense of vector analysis. The most general trilinear self-coupling of the graviton field turns out to be the one derived from the Einstein-Hilbert action plus divergences and coboundaries.