Constrained Dynamics for Quantum Mechanics I. Restricting a Particle to a Surface

Abstract

We analyze constrained quantum systems where the dynamics do not preserve the constraints. This is done in particular for the restriction of a quantum particle in Euclidean n-space to a curved submanifold, and we propose a method of constraining and dynamics adjustment which produces the right Hamiltonian on the submanifold when tested on known examples. This method we hope will become the germ of a full Dirac algorithm for quantum constraints. We take a first step in generalising it to the situation where the constraint is a general selfadjoint operator with some additional structures.

49 pages, TEX, input files amssym.def, amssym.tex

References in corpus (5)

• Coherent State Quantization of Constraint Systems
• Obstructions to Quantization
• Obstruction Results in Quantization Theory
• Monopole Gauge Fields and Quantum Potentials Induced by the Geometry in Simple Dynamical Systems
• Geometrically Induced Gauge Structure on Manifolds Embedded in a Higher Dimensional Space

Cited by in corpus (8)

• Geometric Momentum: the Proper Momentum for a Free Particle on a Two-dimensional Sphere
• Geometric momentum for a particle constrained on a curved hypersurface
• On the Implementation of Constraints through Projection Operators
• Universal Features of Dimensional Reduction Schemes from General Covariance Breaking
• Canonical quantization of motion on submanifolds
• Dynamical chaotic phases and constrained quantum dynamics
• General covariant geometric momentum, gauge potential and a Dirac fermion on a two-dimensional sphere
• Superselection in the presence of constraints