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 struc ture functions is found in the 1-loop (linear in HBAR) approximation o f 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 esta blished in terms of the conserved inner product in the space of physic al states. The global obstructions to this result are briefly discusse d in connection with the ideas of the secondary (third) quantization o f constrained systems.