Hamiltonian Formalism of Particular Bimetric Gravity Model

TL;DR

This paper performs a Hamiltonian analysis of a specific bimetric gravity model, identifying constraints and symmetries, and clarifies the conditions under which the theory exhibits gauge invariance.

Contribution

It provides a detailed Hamiltonian formulation of a particular bimetric gravity model, highlighting the constraints and gauge symmetries involved.

Findings

Eight secondary constraints identified

Four first class constraints under specific potential conditions

First class constraints generate diagonal diffeomorphism

Abstract

In this short note we perform the Hamiltonian analysis of bimetric gravity with one particular form of potential between two metrics. We find that this theory have eight secondary constraints. We identify four constraints that are the first class constraints on condition when the interaction term obeys some specific condition. We show that for the form of the potential studied in this paper this condition is obeyed and hence we can interpret these first class constraints as generators of the diagonal diffeomorphism.