Unified Description of Quantum Mechanics on a Curved Space
Abstract
Starting with the first-order singular Lagrangian, the problem of the quantization of a dynamical system constrained to a submanifold embedded in the higher-dimensional Euclidean space is investigated within the framework of operatorial quantization formalism. Through the projection operator method (POM) with the constraint star-products, it is shown that both of the constraint quantum system with the usual constraint and that with the derivative-type constraint are naturally constructed from one Lagarangian. It is proved that the system with the usual constraint is the sub-system of that with the derivative-type one. Furthermore, the quantization of the dynamical system subject to both of the usual constraint and the derivative-type one is investigated by the POM, and the quantum corrections in the resultant Hamiltonians are discussed.
Keywords
Cite
@article{arxiv.1412.7222,
title = {Unified Description of Quantum Mechanics on a Curved Space},
author = {M. Nakamura},
journal= {arXiv preprint arXiv:1412.7222},
year = {2015}
}
Comments
15 pages, 2 references added, some changes; in sect.3,4