Metric approach to quantum constraints

TL;DR

This paper introduces a novel metric-based framework for deriving equations of motion in constrained quantum systems, extending classical Dirac theory and demonstrating its application with spin-1/2 particle examples.

Contribution

It presents a new approach that generalizes Dirac's classical constraints method to quantum systems, including cases previously unmanageable by Dirac's formalism.

Findings

Framework reduces to quantum Dirac formalism in special cases

Successfully applies to spin-1/2 particles with novel constraints

Handles scenarios beyond traditional Dirac approach

Abstract

A new framework for deriving equations of motion for constrained quantum systems is introduced, and a procedure for its implementation is outlined. In special cases the framework reduces to a quantum analogue of the Dirac theory of constrains in classical mechanics. Explicit examples involving spin-1/2 particles are worked out in detail: in one example our approach coincides with a quantum version of the Dirac formalism, while the other example illustrates how a situation that cannot be treated by Dirac's approach can nevertheless be dealt with in the present scheme.