Abstract

We perform the Batalin-Fradkin-Vilkovisky (BFV) quantization of the 2 + 1 projectable and the 3 + 1 nonprojectable versions of the Horx2c7;ava theory. This is a Hamiltonian formalism, and noncanonical gauges can be used with it. In the projectable case, we show that the integration on canonical momenta reproduces the quantum Lagrangian known from the proof of renormalization of Barvinsky et al. This quantum Lagrangian is nonlocal, its nonlocality originally arose as a consequence of getting regular propagators. The matching of the BFV quantization with the quantum Lagrangian reinforces the program of quantization of the Horx2c7;ava theory. We introduce a local gauge-fixing condition, hence a local Hamiltonian, that leads to the nonlocality of the Lagrangian after the integration. For the case of the nonprojectable theory, this procedure allows us to obtain the complete (nonlocal) quantum Lagrangian that takes into account the second-class constraints. We compare with the integration in general relativity, making clear the relationship between the underlying anisotropic symmetry of the Horx2c7;ava theory and the nonlocality of its quantum Lagrangian.