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

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.