BFV quantization of the nonprojectable 2+1 Horava theory

TL;DR

This paper demonstrates the implementation of BFV quantization in the nonprojectable 2+1 Horava gravity, enabling more flexible gauge choices and advancing the understanding of its canonical structure.

Contribution

It extends the BFV quantization scheme to the nonprojectable 2+1 Horava theory, including nonrelativistic gauges and analyzing its Hamiltonian and constraint structure.

Findings

BFV quantization applied successfully to the nonprojectable Horava theory

Involutive system in Dirac brackets confirmed for the theory

Inclusion of nonlocal gauge conditions from the projectable case

Abstract

We show that the BFV quantization scheme can be implemented in the nonprojectable 2+1 Horava theory. This opens the possibility of imposing more general gauge conditions in the quantization of this theory. The BFV quantization is based on the canonical formalism, which is suitable to incorporate the measure associated to the second-class constraints that the theory has. Special features of the Hamiltonian density and the matrix of second-class constraints allow that the system be involutive in terms of Dirac brackets, which is a nontrivial requisite for implementing the BFV formalism. We present the BRST symmetry transformations in the canonical variables. The theory is of rank one, in the classification introduced by Fradkin and Fradkina. The originally called relativistic gauge-fixing conditions of the BFV formalism can be implemented in the nonprojectable Horava theory, extended to nonrelativistic forms. We show that the nonlocal gauge condition introduced in the projectable theory can be included among these gauges.