Gravity as the Spin-2 Quantum Gauge Theory

TL;DR

This paper develops a quantum gauge theory framework for spin-2 fields, deriving gauge invariance conditions and analyzing graviton interactions, including radiative corrections and long-range behavior in a field-theoretic context.

Contribution

It formulates a gauge-invariant quantum theory of spin-2 fields without relying on geometric assumptions, deriving the graviton self-coupling from the Einstein-Hilbert action within causal perturbation theory.

Findings

The most general graviton self-coupling matches Einstein-Hilbert derived interactions.

Graviton bremsstrahlung processes exhibit logarithmic divergences in the adiabatic limit.

Two-particle scattering with graviton self-energy is finite, matter self-energy diverges logarithmically.

Abstract

This work deals with the theory of a quantized spin-2 field in the framework of causal perturbation theory. It is divided into two parts. In the first part 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 coboundaries and divergences. In the second part of this work (sect.9) we consider a massive scalar field coupled to gravity. We are interested in the long range behaviour of this theory. Radiative corrections for two particle scattering are investigated in the adiabatic limit, where the cutoff of the interaction at infinity is removed. We compute the differential cross section for graviton bremsstrahlung in which one of the scattered particles emits a graviton of low energy. It is shown that such processes are logarithmically divergent in the adiabatic limit. Furthermore we show that the differential cross section for two particle scattering with a graviton self-energy insertion is finite in the adiabatic limit while for matter self-energy it is logarithmically divergent, too.