Constraint Analysis of Linearized Gravity and a Generalization of the HTZ Approach

Abstract

The Dirac constraint formalism is applied to linearized gravity to determine the structure of constraints and construct the canonical Hamiltonian. The diffeomorphism invariance of the Lagrangian is retrieved by a nontrivial generalization of the method of Henneaux, Teitelboim and Zanelli, which takes into account the appearance of spatial derivatives of constraints in the constraint structure. A couple of first order formulations of the theory are discussed with the hope of opening avenues on an unambiguous canonical treatment of the Einstein-Hilbert action in its first order form.