DIRAC AND BFV QUANTIZATION METHODS IN THE 1-LOOP APPROXIMATION - CLOSURE OF THE QUANTUM CONSTRAINT ALGEBRA AND THE CONSERVED INNER-PRODUCT

Operator realization of quantum constraints and the lowest-order structure functions is found in the 1-loop (linear in HBAR) approximation of the Dirac and BFV quantization for the general gauge theory subject to first-class constraints. Semiclassical equivalence of the Dirac and BFV methods to the reduced quantization of physical variables is established in terms of the conserved inner product in the space of physical states. The global obstructions to this result are briefly discussed in connection with the ideas of the secondary (third) quantization of constrained systems.