Operator ordering for generally covariant systems

TL;DR

This paper investigates the ordering of operators in generally covariant systems using the BRST formalism, focusing on quadratic Hamiltonian constraints and the construction of inner products for systems with intrinsic or extrinsic time.

Contribution

It introduces a method to determine operator orderings for quadratic constraints within the BRST framework, including potential factorization and inner product construction.

Findings

Operator ordering consistent with gauge invariance established.

Inner product construction for systems with different time types analyzed.

Framework applicable to a broad class of covariant systems.

Abstract

The constraint operators belonging to a generally covariant system are found out within the framework of the BRST formalism. The result embraces quadratic Hamiltonian constraints whose potential can be factorized as a never null function times a gauge invariant function. The building of the inner product between physical states is analyzed for systems featuring either intrinsic or extrinsic time.