  Quantum localization of classical mechanics within the BRST-BFV and BV (or
field-antifield) quantization methods are studied. It is shown that a special
choice of gauge fixing functions (or BRST-BFV charge) together with the unitary
limit leads to Hamiltonian localization in the path integral of the BRST-BFV
formalism. In turn, we find that a special choice of gauge fixing functions
being proportional to extremals of an initial non-degenerate classical action
together with a very special solution of the classical master equation result
in Lagrangian localization in the partition function of the BV formalism.
