Quantum Lagrangian of the Hořava theory and its nonlocalities

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