Constrained quantum dynamics

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.