Covariant BRST Quantization of Unimodular Gravity II -- Formulation with a vector antighost --

TL;DR

This paper presents a simplified covariant BRST quantization of unimodular gravity using a vector antighost, maintaining the same physical degrees of freedom as general relativity and reducing ghost complexity.

Contribution

An alternative formulation of covariant BRST quantization of unimodular gravity using a vector antighost instead of tensor fields, simplifying the ghost sector.

Findings

Simpler covariant quantization with fewer ghosts.

No tripole modes in the ghost sector.

Two physical transverse modes as in general relativity.

Abstract

In our previous paper, we have presented a covariant BRST quantization of unimodular gravity which may account for the smallness of the cosmological constant, and have shown that the physical degrees of freedom in the theory are the same as general relativity. The formulation has been given by using rank-2 antisymmetric tensor fields for both ghosts and antighosts. Here we give an alternative formulation using a vector field for the antighost but keeping the same structure for the ghosts. This gives a significantly simpler covariant quantization with less ghosts and no tripole modes in the ghost sector. We show that this also gives only two physical transverse modes as in general relativity.