Saved in:
| Main Author: | |
|---|---|
| Format: | Artículo científico |
| Language: | en |
| Published: |
Sociedade Brasileira de Física
2005
|
| Subjects: | |
| Online Access: | https://www.redalyc.org/articulo.oa?id=46435219 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- The classical and commutative limits of noncommutative quantum mechanics: A superstar wigner-moyal equation Ardeshir Eftekharzadeh B. L. Hu Física, Astronomía y Matemáticas We are interested in the similarities and differences between the quantum-classical (Q-C) and thenoncommutative-commutative (NC-Com) correspondences. As one useful platform to address this issue wederive the superstar Wigner-Moyal equation for noncommutative quantum mechanics (NCQM). A superstarF-product combines the usual phase space ¤ star and the noncommutative ? star-product. Having dealt withsubtleties of ordering present in this problem we show that theWeyl correspondence of the NC Hamiltonian hasthe same form as the original Hamiltonian, but with a non-commutativity parameter q-dependent, momentumdependentshift in the coordinates. Using it to examine the classical and the commutative limits, we find thatthere exist qualitative differences between these two limits. Specifically, if q 6= 0 there is no classical limit.Classical limit exists only if q!0 at least as fast as ~!0, but this limit does not yield Newtonian mechanics,unless the limit of q=~ vanishes as q!0. For another angle towards this issue we formulate the NC version ofthe continuity equation both from an explicit expansion in orders of q and from a Noethers theorem conservedcurrent argument. We also examine the Ehrenfest theorem in the NCQM context. 2005 artículo científico 0103-9733 https://www.redalyc.org/articulo.oa?id=46435219 en http://www.redalyc.org/revista.oa?id=464 Brazilian Journal of Physics application/pdf Sociedade Brasileira de Física Brazilian Journal of Physics (Brasil) Num.2A Vol.35