Canonical quantization of motion on submanifolds

TL;DR

This paper reviews canonical quantization methods for free particles constrained to curved submanifolds, discussing previous work and presenting new results in the context of second class constraints.

Contribution

It provides a comprehensive review and extension of canonical quantization techniques for particles on curved submanifolds, including new findings.

Findings

Enhanced quantization methods for submanifold motion

New results on second class constraints

Clarification of previous quantization approaches

Abstract

This is an extended version of the talk given by the Author at the 40th Symposium on Mathematical Physics held in Torun, Poland, June 25-28, 2008. We review the methods of canonical quantization of free particle motion on curved submanifolds considered as a system with second class constraints. The work is based on our previous articles, quant-ph/0508044 and quant-ph/0508111. However, some new results are also presented.