|
| related topics |
| {equation, function, exp} |
| {field, particle, equation} |
| {energy, gaussian, time} |
| {operator, operators, space} |
| {phase, path, phys} |
| {group, space, representation} |
| {vol, operators, histories} |
| {cos, sin, state} |
|
The conformally invariant Laplace-Beltrami operator and factor ordering
Michael P. Ryan, Alexander V. Jr.
abstract: In quantum mechanics the kinetic energy term for a single particle is usually
written in the form of the Laplace-Beltrami operator. This operator is a factor
ordering of the classical kinetic energy. We investigate other relatively
simple factor orderings and show that the {\it only} other solution for a
conformally flat metric is the conformally invariant Laplace-Beltrami operator.
For non-conformally-flat metrics this type of factor ordering fails, by just
one term, to give the conformally invariant Laplace-Beltrami operator.
- oai_identifier:
- oai:arXiv.org:quant-ph/0406167
- categories:
- quant-ph gr-qc hep-th math-ph math.MP
- comments:
- 7 pages, extra paraghraph and two references are added
- doi:
- 10.1016/j.physleta.2004.10.021
- arxiv_id:
- quant-ph/0406167
- journal_ref:
- Phys.Lett. A333 (2004) 30-34
- report_no:
- Preprint ICN-UNAM 04-06
- created:
- 2004-06-22
- updated:
- 2004-10-21
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