Hamiltonian analysis of non-chiral Plebanski theory and its generalizations

Abstract

We consider the non-chiral, full Lorentz group-based Plebanski formulation of general relativity in its version that utilizes the Lagrange multiplier field Φ with ‘internal’ indices. The Hamiltonian analysis of this version of the theory turns out to be simpler than in the previously considered in the literature version with Φ carrying spacetime indices. We then extend the Hamiltonian analysis to a more general class of theories whose action contains scalar invariants constructed from Φ. Such theories have recently been considered in the context of unification of gravity with other forces. We show that these more general theories have six additional propagating degrees of freedom as compared to general relativity. This has not been appreciated in the literature treating them as being not much different from GR.