BFV quantization of the nonprojectable (2+1)-dimensional Horava theory

We show that the Batalin-Fradkin-Vilkovisky (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 Becchi-Rouet-Stora-Tyutin 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 Hofava theory, extended to nonrelativistic forms. We show that the nonlocal gauge condition introduced in the projectable theory can be included among these gauges.

Automated summary

This study demonstrates the implementation of the BFV quantization scheme in the nonprojectable (2 + 1)-Horava theory, allowing for the imposition of more general gauge conditions. The special features of the Hamiltonian density and the matrix of second-class constraints play a crucial role in achieving involutiveness of the system in terms of Dirac brackets, a nontrivial requisite for implementing the BFV formalism.