Fast Poisson brackets and constraint algebras in canonical gravity

TL;DR

This paper introduces a computer algebra package that simplifies the computation of Poisson brackets and constraint algebras in canonical gravity, aiding the analysis of gauge symmetries and pathologies in various gravity theories.

Contribution

The authors develop and validate an efficient computer algebra tool for computing Poisson brackets and reconstructing constraint algebras in canonical gravity, including modified theories.

Findings

Successfully applied to pure general relativity

Effective in analyzing modified gravity theories

Facilitates the detection of gauge symmetries and pathologies

Abstract

In the study of alternative or extended theories of gravity, Dirac's Hamiltonian constraint algorithm is invaluable for enumerating the propagating modes and gauge symmetries. For gravity, this canonical approach is frequently applied as a means for finding pathologies such as strongly coupled modes; more generally it facilitates the reconstruction of gauge symmetries and the quantization of gauge theories. For gravity, however, the algorithm can become notoriously arduous to implement. We present a simple computer algebra package for efficiently computing Poisson brackets and reconstructing constraint algebras. The tools are stress-tested against pure general relativity and modified gravity, including the order reduction of general relativity at two loops.