Gauge invariance and second class constraints in three-dimensional linearized massive gravity

Abstract

A recently introduced approach for the dynamical analysis and quantization of field theoretical models with second class constraints is illustrated in the context of linearized gravity in 3D. The canonical structures of the intermediate and the self-dual models linearized gravity in 3D are discussed in detail. It is shown that the first order self-dual model whose constraints are all second class may be regarded as a gauge fixed version of the second order gauge invariant intermediate model. In particular it is shown how to construct the gauge invariant Hamiltonian of the intermediate model starting from the Hamiltonian of the self-dual model. The relation with the topologically massive linearized gravity is also discussed.