Analysis of constraints and their algebra in bimetric theory

TL;DR

This paper conducts a canonical analysis of bimetric theory, explicitly computing constraints and their algebra to understand the elimination of ghosts and the role of covariance in defining the spacetime metric.

Contribution

It provides the first explicit computation of the secondary constraint and clarifies how the covariance algebra influences the spacetime metric in bimetric theory.

Findings

Identified a secondary constraint that eliminates the ghost.

Found four first class constraints generating the covariance algebra.

Showed the spacetime metric depends on the choice of constraints.

Abstract

We perform a canonical analysis of the bimetric theory in the metric formulation, computing the constraints and their algebra explicitly. In particular, we compute a secondary constraint, that has been argued to exist earlier, and show that it has the correct form to eliminate the ghost. We also identify a set of four first class constraints that generate the algebra of general covariance. The covariance algebra naturally determines a spacetime metric for the theory. However, in bimetric theory, this metric is not unique but depends on how the first class constraints are identified.