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.Comment: 16 page