SOLUTION OF QUANTUM DIRAC CONSTRAINTS VIA PATH-INTEGRAL

The semiclassical solution of quantum Dirac constraints in a generic c onstrained system is obtained by directly calculating in the one-loop approximation the gauge field path integral with a relativistic gauge- fixing procedure. The gauge independence property of this path integra l is analyzed by the method of Ward identities with special emphasis o n boundary conditions for the gauge fields. The calculations are based on the known reduction algorithms for functional determinants extende d to gauge theories. The mechanism of transition from relativistic gau ge conditions to unitary gauges, participating in the construction of this solution, is explicitly revealed. Implications of this result in problems with space-time boundaries, quantum gravity and cosmology are briefly discussed. (C) 1998 Elsevier Science B.V.