Geometric Potential Resulting from Dirac Quantization

Abstract

A fundamental problem regarding the Dirac quantization of a free particle on an $N-1$ curved hypersurface embedded in $N$($\ge 2$) 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. We resolve this problem by means of 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.

5 pages, 0 figure. corrected typos. arXiv admin note: text overlap with arXiv:1701.08370

References in corpus (4)

• Quantum mechanics on curved 2D systems with electric and magnetic fields
• Geometric influences of a particle confined to a curved surface embedded in three-dimensional Euclidean space
• Bilayer graphene Origami: curvature-induced p-n junctions
• The centripetal force law and the equation of motion for a particle on a curved hypersurface

Cited by in corpus (8)

• Curved non-interacting two-dimensional electron gas with anisotropic mass
• No existence of the geometric potential for a Dirac fermion on two-dimensional curved surfaces of revolution
• General covariant geometric momentum, gauge potential and a Dirac fermion on a two-dimensional sphere
• Hamiltonian and Lagrangian BRST quantization in Riemann Manifold
• The curvature-induced gauge potential and the geometric momentum for a particle on a hypersphere
• Geometric momentum and angular momentum for charge-monopole system
• Hamiltonian and Lagrangian BRST quantization in Riemann Manifold II
• Generally covariant geometric momentum and geometric potential for a Dirac fermion on a two-dimensional hypersurface