|
| related topics |
| {group, space, representation} |
| {operator, operators, space} |
| {equation, function, exp} |
| {state, states, coherent} |
| {energy, gaussian, time} |
| {field, particle, equation} |
| {cos, sin, state} |
|
W(infty)-Covariance of the Weyl-Wigner-Groenewold-Moyal Quantization
T. Dereli, A. Vercin
abstract: The differential structure of operator bases used in various forms of the
Weyl-Wigner-Groenewold-Moyal (WWGM) quantization is analyzed and a
derivative-based approach, alternative to the conventional integral-based one
is developed. Thus the fundamental quantum relations follow in a simpler and
unified manner. An explicit formula for the ordered products of the
Heisenberg-Weyl algebra is obtained. The W(infty) -covariance of the
WWGM-quantization in its most general form is established. It is shown that the
group action of W(infty) that is realized in the classical phase space induces
on bases operators in the corresponding Hilbert space a similarity
transformation generated by the corresponding quantum W(infty) which provides a
projective representation of the former $W_{\infty}$. Explicit expressions for
the algebra generators in the classical phase space and in the Hilbert space
are given. It is made manifest that this W(infty)-covariance of the
WWGM-quantization is a genuine property of the operator bases.
- oai_identifier:
- oai:arXiv.org:quant-ph/9707040
- categories:
- quant-ph
- comments:
- 14 pages, Latex file. No figures. To apear in J. Math. Phys
- doi:
- 10.1063/1.532149
- arxiv_id:
- quant-ph/9707040
- journal_ref:
- J.Math.Phys. 38 (1997) 5515-5530
- created:
- 1994-07-21
Full article ▸
|
|
| related documents |
| 0503041v2 |
| 0604153v1 |
| 0004031v3 |
| 0110152v1 |
| 0506222v1 |
| 9702028v1 |
| 0602189v1 |
| 0507094v1 |
| 9805084v1 |
| 0102018v1 |
| 0206012v1 |
| 0202050v3 |
| 0011021v2 |
| 0601076v1 |
| 0510156v1 |
| 0010082v2 |
| 0307019v1 |
| 0501104v4 |
| 0605026v1 |
| 9711036v2 |
| 0009033v1 |
| 0612096v1 |
| 0305150v1 |
| 0410209v1 |
| 0604202v1 |
|