ADM formulation and Hamiltonian analysis of $f(Q)$ gravity

TL;DR

This paper performs a Hamiltonian analysis of $f(Q)$ gravity, revealing it has 8 physical degrees of freedom and that gauge fixing breaks its diffeomorphism symmetry, with implications for mode decomposition.

Contribution

It provides the first Hamiltonian analysis of $f(Q)$ gravity with gauge fixing, identifying its degrees of freedom and symmetry properties.

Findings

$f(Q)$ gravity has 8 physical degrees of freedom.

Diffeomorphism symmetry is fully broken by gauge fixing.

Discussion of mode decomposition of degrees of freedom.

Abstract

$f(Q)$ gravity is an extension of the symmetric teleparallel equivalent to general relativity. We demonstrate the Hamiltonian analysis of $f(Q)$ gravity with fixing the coincident gauge condition. Using the standard Dirac-Bergmann algorithm, we show that $f(Q)$ gravity has 8 physical degrees of freedom. This result reflects that the diffeomorphism symmetry of $f(Q)$ gravity is completely broken due to the gauge fixing. Moreover, in terms of the perturbations, we discuss the possible mode decomposition of these degrees of freedom.