Quantum Dirac constraints, Ward identities and path integral in relativistic gauge

TL;DR

This paper develops a method to solve quantum Dirac constraints in gauge theories using path integrals with relativistic gauge fixing, revealing the transition mechanism to unitary gauges via Ward identities.

Contribution

It introduces a reduction algorithm for functional determinants in gauge theories and elucidates the transition from relativistic to unitary gauges through Ward identities.

Findings

Path integral with relativistic gauge fixing is explicitly calculated.

Reduction algorithms for functional determinants are extended to gauge theories.

Transition mechanism from relativistic to unitary gauges is clarified.

Abstract

Quantum Dirac constraints in generic constrained system are solved by directly calculating in the one-loop approximation the path integral with relativistic gauge fixing procedure. The calculations are based on the reduction algorithms for functional determinants extended to gauge theories. Explicit mechanism of transition from relativistic gauge conditions to unitary gauges, participating in the construction of this solution, is revealed by the method of Ward identities.