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Geometric momentum for a particle constrained on a curved hypersurface
- Source :
- J. Math. Phys. 54, 122113 (2013)
- Publication Year :
- 2013
-
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.<br />Comment: 5 pages, no figure
- Subjects :
- Quantum Physics
Mathematical Physics
Subjects
Details
- Database :
- arXiv
- Journal :
- J. Math. Phys. 54, 122113 (2013)
- Publication Type :
- Report
- Accession number :
- edsarx.1305.0970
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1063/1.4854075