  Correspondence between BRST-BFV, Dirac and refined algebraic (group
averaging, projection operator) approaches to quantize constrained systems is
analyzed. For the closed-algebra case, it is shown that the component of the
BFV wave function with maximal (minimal) number of ghosts and antighosts in the
Schrodinger representation may be viewed as a wave function in the refined
algebraic (Dirac) quantization approach. The Giulini-Marolf group averaging
formula for the inner product in the refined algebraic quantization approach is
obtained from the Batalin-Marnelius prescription for the BRST-BFV inner product
which should be generally modified due to topological problems. The considered
prescription for the correspondence of states is observed to be applicable to
the open-algebra case. Refined algebraic quantization approach is generalized
then to the case of nontrivial structure functions. A simple example is
discussed. Correspondence of observables in different quantization methods is
also investigated.
