General Covariant Gauge Fixing for Massless Spin-Two Fields

TL;DR

This paper explores the most general covariant gauge fixing for massless spin-two fields, revealing limitations of standard gauges and proposing a non-quadratic gauge fixing approach to achieve a traceless-transverse propagator, with implications for gravitational field analysis.

Contribution

It introduces a non-quadratic gauge fixing Lagrangian for spin-two fields that yields a traceless-transverse propagator, expanding the gauge fixing options beyond traditional Faddeev-Popov methods.

Findings

Standard gauges cannot produce a traceless-transverse propagator simultaneously.

A non-quadratic gauge fixing Lagrangian introduces additional ghost fields.

Application to gravitational energy-momentum tensor at finite temperature.

Abstract

The most general covariant gauge fixing Lagrangian is considered for a spin-two gauge theory in the context of the Faddeev-Popov procedure. In general, five parameters characterize this gauge fixing. Certain limiting values for these parameters give rise to a spin-two propagator that is either traceless or transverse, but for no values of these parameters is this propagator simultaneously traceless and transverse. Having a traceless-transverse (TT) propagator ensures that only the physical degrees of freedom associated with the tensor field propagate, and hence it is analogous to the Landau gauge in electrodynamics. To obtain such a traceless-transverse propagator, a gauge fixing Lagrangian which is not quadratic must be employed; this sort of gauge fixing Lagrangian is not encountered in the usual Faddeev-Popov procedure. It is shown that when this non-quadratic gauge fixing Lagrangian is used, two Fermionic and one Bosonic ghost arise. As a simple application we discuss the energy-momentum tensor of the gravitational field at finite temperature.