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| related topics |
| {group, space, representation} |
| {operator, operators, space} |
| {energy, gaussian, time} |
| {equation, function, exp} |
| {classical, space, random} |
| {particle, mechanics, theory} |
| {phase, path, phys} |
| {observables, space, algebra} |
| {cos, sin, state} |
|
Generalized Weyl-Wigner map and Vey quantum mechanics
Nuno Costa Dias, Joao Nuno Prata
abstract: The Weyl-Wigner map yields the entire structure of Moyal quantum mechanics
directly from the standard operator formulation. The covariant generalization
of Moyal theory, also known as Vey quantum mechanics, was presented in the
literature many years ago. However, a derivation of the formalism directly from
standard operator quantum mechanics, clarifying the relation between the two
formulations is still missing. In this paper we present a covariant
generalization of the Weyl order prescription and of the Weyl-Wigner map and
use them to derive Vey quantum mechanics directly from the standard operator
formulation. The procedure displays some interesting features: it yields all
the key ingredients and provides a more straightforward interpretation of the
Vey theory including a direct implementation of unitary operator
transformations as phase space coordinate transformations in the Vey idiom.
These features are illustrated through a simple example.
- oai_identifier:
- oai:arXiv.org:quant-ph/0102018
- categories:
- quant-ph
- comments:
- 15 pages, LaTeX
- arxiv_id:
- quant-ph/0102018
- journal_ref:
- J. Math. Phys. 42 (2001) 5565-5579
- created:
- 2001-02-03
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