arXiv:2102.04595v1 [hep-th] 9 Feb 2021 BFV quantization of the nonprojectable 2+1 Hoˇ rava theory Jorge Bellor´ ın 1 and Byron Droguett 2 Department of Physics, Universidad de Antofagasta, 1240000 Antofagasta, Chile. 1 jbellori@gmail.com, 2 byron.droguett@ua.cl Abstract We show that the BFV quantization scheme can be implemented in the nonpro- jectable 2+1 Hoˇ rava 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 Hamil- tonian 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 imple- menting 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 Hoˇ rava theory, extended to nonrelativistic forms. We show that the nonlocal gauge condition in- troduced in the projectable theory can be included among these gauges.