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arXiv:1212.6373 · Annals of Physics

Quantum motion on a torus as a submanifold problem in a generalized Dirac’s theory of second-class constraints

D. M. Xun, Quanhui Liu, Xuanmin Zhu

Published Aug 10, 2013• 30 citations
arXivHTMLPDF
DOI
10.1016/j.aop.2013.07.008

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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 Rn to a curved submanifold, and we propose a method of constraining and dynamics adjustment that produces the right Hamiltonian on the submanifold when tested on known examples. This method will be the germ of a “Dirac algorithm for quantum constraints.” We generalize it to the situation where the constraint is a general self-adjoint operator with some additional structures.