Consistency of the Hamiltonian formulation of the lowest-order effective action of the complete Horava theory

TL;DR

This paper conducts a Hamiltonian analysis of the lowest-order effective action of the complete Horava theory, revealing its constraint structure, degrees of freedom, and the behavior of the Hamiltonian constraint.

Contribution

It provides a detailed Hamiltonian formulation of the complete Horava theory, including the invariant terms proposed by Blas, Pujolas, and Sibiryakov, and analyzes the constraint algebra and degrees of freedom.

Findings

Constraint algebra closes consistently.

The Hamiltonian constraint is second-class and elliptic.

The model has six propagating degrees of freedom.

Abstract

We perform the Hamiltonian analysis for the lowest-order effective action, up to second order in derivatives, of the complete Horava theory. The model includes the invariant terms that depend on \partial_i ln N proposed by Blas, Pujolas and Sibiryakov. We show that the algebra of constraints closes. The "Hamiltonian" constraint is of second-class behavior and it can be regarded as an elliptic partial differential equation for N. The linearized version of this equation is a Poisson equation for N that can be solved consistently. The preservation in time of the Hamiltonian constraint yields an equation that can be consistently solved for a Lagrange multiplier of the theory. The model has six propagating degrees of freedom in the phase space, corresponding to three even physical modes. When compared with the \lambda R model studied by us in a previous paper, it lacks two second-class constraints, which leads to the extra even mode.