Abstract

We present an analysis on the Becchi-Rouet-Stora-Tyutin (BRST) symmetry transformations of the Horava theory under the Batalin-Fradkin-Vilkovisky quantization, both in the nonprojectable and projectable cases. We obtain that the BRST transformations are intimately related to a particular spatial diffeomorphism along one of the ghost vector fields. We show explicitly the invariance of the quantum action and the nilpotence of the BRST transformations, using this diffeomorphism largely. The BRST symmetry is verified in the whole phase space, inside and outside the constrained surface. When restricted to the constrained surface, the BRST transformations are completely local. The consistency of the BRST symmetry is a fundamental feature of a quantum field theory, specially for renormalization. The BFV quantization is independent of the chosen gauge-fixing condition. This allows us to study the unitarity of the quantum Horava theory, covering the gauge required for renormalization. We prove that, if the solution for the lapse function exists, then the unitarity of the theory is established.