Hamiltonian Analysis of non-chiral Plebanski Theory and its Generalizations

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.

10 pages

References in corpus (3)

• On deformations of Ashtekar's constraint algebra
• Renormalizable Non-Metric Quantum Gravity?
• Plebanski Theory and Covariant Canonical Formulation

Cited by in corpus (11)

• $BF$ gravity
• Bi-metric theory of gravity from the non-chiral Plebanski action
• Towards effective actions for the continuum limit of spin foams
• A Unified Theory of Non-Linear Electrodynamics and Gravity
• Lorentz-covariant Hamiltonian analysis of BF gravity with the Immirzi parameter
• Spherically symmetric black holes in minimally modified self-dual gravity
• Spin connection formulations of real Lorentzian General Relativity
• Pure Lorentz spin connection theories and uniqueness of General Relativity
• Polysymplectic formulation for BF gravity with Immirzi parameter
• From area metric backgrounds to the cosmological constant and corrections to the Polyakov action
• Canonical analysis of unimodular Plebański gravity