Solution of quantum Dirac constraints via path integral

TL;DR

This paper presents a semiclassical method for solving quantum Dirac constraints using gauge field path integrals, emphasizing gauge independence and boundary conditions, with implications for quantum gravity and cosmology.

Contribution

It introduces a direct calculation approach for quantum Dirac constraints via path integrals with relativistic gauge fixing, highlighting gauge independence and boundary effects.

Findings

Path integral approach yields gauge-independent solutions.

Explicit transition mechanism from relativistic to unitary gauges.

Implications for quantum gravity and cosmology discussed.

Abstract

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.