Effective Constraints for Quantum Systems

TL;DR

This paper introduces an effective formalism for quantum constrained systems that simplifies deriving solutions and observables without needing full knowledge of the physical inner product, using an infinite system of constraint functions.

Contribution

It presents a novel approach using constraint functions on quantum phase space, enabling manageable solutions for constrained quantum systems without full inner product knowledge.

Findings

Applicable to linear constraints and non-relativistic particles

Simplifies derivation of solutions and observables

Handles physical reality conditions effectively

Abstract

An effective formalism for quantum constrained systems is presented which allows manageable derivations of solutions and observables, including a treatment of physical reality conditions without requiring full knowledge of the physical inner product. Instead of a state equation from a constraint operator, an infinite system of constraint functions on the quantum phase space of expectation values and moments of states is used. The examples of linear constraints as well as the free non-relativistic particle in parameterized form illustrate how standard problems of constrained systems can be dealt with in this framework.