Constrained Dynamics for Quantum Mechanics I. Restricting a Particle to a Surface
High Energy Physics - Theory
2008-11-26 v1
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.
Cite
@article{arxiv.hep-th/9712052,
title = {Constrained Dynamics for Quantum Mechanics I. Restricting a Particle to a Surface},
author = {Hendrik Grundling and C. A. Hurst},
journal= {arXiv preprint arXiv:hep-th/9712052},
year = {2008}
}
Comments
49 pages, TEX, input files amssym.def, amssym.tex