Gauge Invariance and Second Class Constraints in 3-D Linearized Gravity

TL;DR

This paper applies a new method for analyzing and quantizing field theories with second class constraints to 3-D linearized gravity, revealing gauge invariance structures and relations between different models.

Contribution

It demonstrates how to relate the self dual and intermediate models of 3-D linearized gravity using a novel approach for second class constraints.

Findings

The self dual model can be seen as a gauge-fixed version of the intermediate model.

A gauge invariant Hamiltonian for the intermediate model is constructed.

The relation to topologically massive linearized gravity is discussed.

Abstract

A recently introduced approach for the dynamical analysis and quantization of field theoretical models with second class constraints is ilustrated applied to linearized gravity in 3-D. The canonical structure of two different models of linerized gravity in 3-D, the intermediate and the self dual models, is 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 one of the self dual model. The relation with the t opologically massive linearized gravity is also discussed.