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arXiv · 1305.0970

Geometric momentum for a particle constrained on a curved hypersurface

Q. H. Liu
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Abstract

A strengthened canonical quantization scheme for the constrained motion on a curved hypersurface is proposed with introduction of the second category of fundamental commutation relations between Hamiltonian and positions/momenta, whereas those between positions and moments are categorized into the first. As an $N-1$ ($N\geq2$) dimensional hypersurface is embedded in an N dimensional Euclidean space, we obtain the proper momentum that depends on the mean curvature. For the surface is the spherical one, a long-standing problem on the form of the geometric potential is resolved in a lucid and unambiguous manner, which turns out to be identical to that given by the so-called confining potential technique. In addition, a new dynamical group SO(N,1) symmetry for the motion on the sphere is demonstrated.

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Q. H. Liu. 2013-05-04. Geometric momentum for a particle constrained on a curved hypersurface. https://doi.org/10.1063/1.4854075

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