Hamiltonian Analysis of non-chiral Plebanski Theory and its Generalizations

TL;DR

This paper performs a Hamiltonian analysis of non-chiral Plebanski formulations of general relativity, revealing additional degrees of freedom in generalized theories relevant to unification efforts.

Contribution

It simplifies the Hamiltonian analysis of non-chiral Plebanski theory and extends it to a broader class of theories with scalar invariants, uncovering extra propagating degrees of freedom.

Findings

Hamiltonian analysis is simpler for the non-chiral Lorentz group formulation.

Generalized theories contain six additional propagating degrees of freedom.

These theories differ significantly from general relativity in their dynamical content.

Abstract

We consider non-chiral, full Lorentz group-based Plebanski formulation of general relativity in its version that utilizes the Lagrange multiplier field Phi 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 Phi carrying spacetime indices. We then extend the Hamiltonian analysis to a more general class of theories whose action contains scalars invariants constructed from Phi. 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, something that has not been appreciated in the literature treating them as being not much different from GR.