  The semiclassical solution of quantum Dirac constraints in generic
constrained system is obtained by directly calculating in the one-loop
approximation the gauge field path integral with relativistic gauge fixing
procedure. The gauge independence property of this path integral is analyzed by
the method of Ward identities with a special emphasis on boundary conditions
for gauge fields. The calculations are based on the known reduction algorithms
for functional determinants extended to gauge theories. The mechanism of
transition from relativistic gauge conditions to unitary gauges, participating
in the construction of this solution, is explicitly revealed. Implications of
this result in problems with spacetime boundaries, quantum gravity and
cosmology are briefly discussed.
