Dirac quantization of free motion on curved surfaces

Abstract

We give an explicit operator realization of Dirac quantization of free particle motion on a surface of codimension 1. It is shown that the Dirac recipe is ambiguous and a natural way of fixing this problem is proposed. We also introduce a modification of Dirac procedure which yields zero quantum potential. Some problems of abelian conversion quantization are pointed out.

16 pages

Cited by in corpus (5)

• Geometric Momentum: the Proper Momentum for a Free Particle on a Two-dimensional Sphere
• Canonical quantization of motion on submanifolds
• Thin layer quantization in higher dimensions and codimensions
• 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