Geometric Potential and Dirac Quantization |
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| Authors: | Dingkun Lian Liangdong Hu Quanhui Liu |
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| Affiliation: | 1. School for Theoretical Physics, School of Physics and Electronics, Hunan University, Changsha, China;2. Synergetic Innovation Center for Quantum Effects and Applications (SICQEA), Hunan Normal University, Changsha, China |
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| Abstract: | A fundamental problem regarding the Dirac quantization of a free particle on an  ( ) curved hypersurface embedded in N flat space is the impossibility to give the same form of the curvature‐induced quantum potential, the geometric potential as commonly called, as that given by the Schrödinger equation method where the particle moves in a region confined by a thin‐layer sandwiching the surface. This problem is resolved by means of a previously proposed scheme that hypothesizes a simultaneous quantization of positions, momenta, and Hamiltonian, among which the operator‐ordering‐free section is identified and is then found sufficient to lead to the expected form of geometric potential. |
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| Keywords: | constrained Hamiltonian geometric momentum geometric potential hypersurfaces quantization |
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) curved hypersurface embedded in N flat space is the impossibility to give the same form of the curvature‐induced quantum potential, the geometric potential as commonly called, as that given by the Schrödinger equation method where the particle moves in a region confined by a thin‐layer sandwiching the surface. This problem is resolved by means of a previously proposed scheme that hypothesizes a simultaneous quantization of positions, momenta, and Hamiltonian, among which the operator‐ordering‐free section is identified and is then found sufficient to lead to the expected form of geometric potential.