Constrained quantum dynamics

TL;DR

This paper reviews two methods for describing the dynamics of constrained quantum systems, highlighting their differences and providing illustrative examples of nonlinear motion caused by constraints.

Contribution

It introduces and compares the symplectic and metric formulations for constrained quantum dynamics, a novel synthesis of classical and quantum approaches.

Findings

Both methods effectively describe constrained quantum systems.

Examples demonstrate nonlinear motion due to constraints.

The metric approach is purely quantum with no classical counterpart.

Abstract

We give an overview of the two different methods that have been introduced in order to describe the dynamics of constrained quantum systems; the symplectic formulation and the metric formulation. The symplectic method extends the work of Dirac on constrained classical systems to quantum systems, whereas the metric approach is purely a quantum mechanical method having no immediate classical counterpart. Two examples are provided that illustrate the nonlinear motion induced by the constraint.