Noncommutative Quantum Gravity

TL;DR

This paper explores the BRST and anti-BRST symmetries in noncommutative perturbative quantum gravity, analyzing gauge fixing, ghost terms, and unitarity issues introduced by mass terms.

Contribution

It introduces the formulation of BRST and anti-BRST symmetries in noncommutative quantum gravity and examines their invariance and unitarity properties.

Findings

BRST and anti-BRST invariance of the combined Lagrangian in noncommutative spacetime

Analysis of gauge fixing and ghost terms in different gauges

Unitarity violation due to mass term in noncommutative BRST framework

Abstract

We discuss the BRST and anti-BRST symmetries for perturbative quantum gravity in noncommutative spacetime. In this noncommutative perturbative quantum gravity the sum of the classical Lagrangian density with a gauge fixing term and a ghost term is shown to be invariant the noncommutative BRST and the noncommutative anti-BRST transformations. We analyse the gauge fixing term and the ghost term in both linear as well as non-linear gauges. We also discuss the unitarity evolution of the theory and analyse the violation of unitarity of by introduction of a bare mass term in the noncommutative BRST and the noncommutative anti-BRST transformations.