On the Relation between Operator Constraint --, Master Constraint --, Reduced Phase Space --, and Path Integral Quantisation

Understand

Path integral formulations for gauge theories must start from the canonical formulation in order to obtain the correct measure.

• A possible avenue to derive it is to start from the reduced phase space formulation.
• In this article we review this rather involved procedure in full generality.
• Moreover, we demonstrate that the reduced phase space path integral formulation formally agrees with the Dirac's operator constraint quantisation and, more specifically, with the Master constraint quantisation for first class constraints.