Noncommutative configuration space. Classical and quantum mechanical aspects

Brazilian Journal of Physics

Volumn 36, Issue 1 B, 2006, Pages 194-207

  Vanhecke, F J ^a   Sigaud, C ^a   Da Silva, A R ^a  

^a FEDERAL UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

Noncommutativity; Quantization; Symplectic mechanics

Indexed keywords

EID: 33645780179     PISSN: 01039733     EISSN: 01039733     Source Type: Journal    
DOI: 10.1590/S0103-97332006000200012     Document Type: Conference Paper

References (33)

1. J. von Neumann, Math. Annalen 104, 570 (1931).
2. R. Peierls, Z. Phys. 80, 763 (1933).
3. H. S. Snyder, Phys. Rev. 71, 38 (1947).
4. A. Messiah, Mécanique Quantique 1, Dunod, 1962.
5. J-M. Souriau, Structure des systèmes dynamiques, Dunod, 1970.
6. R. Abraham and J. E. Marsden, Foundations of Mechanics, Benjamin, 1978
7. M. J. Gotay, J. M. Nester, and G. Hinds, J. Math. Phys. 19, 2388 (1978).
8. A.P. Balachandran, G. Marmo, B-S. Skagerstam, and A. Stern, Gauge Symmetries and Fibre Bundles, Lect. Notes in Physics 188 (1983).
9. V. Guillemin and S. Sternberg, Symplectic Tecniques in Physics, Cambridge University Press, 1984.
10. S. Doplicher, K. Fredenhagen, and J. Roberts, Comm. Math. Phys. 172, 187 (1995).
11. C. Duval and P. A. Horváthy, Phys. Lett. B 479, 284 (2000).
12. V. P. Nair and A. Polychronakos, Phys. Lett. B 505, 267 (2001).
13. B. Morariu, and A. Polychronakos, Nucl. Phys. B 610, 531 (2001)
14. and Nucl. Phys. B 634, 326 (2002).
15. P. A. Horváthy, Ann. Phys. 299, 128 (2002).
16. A. E. F. Djemaï and H. Smail, arXiv:hep-th/0309006(2003).
17. A. Bérard and H. Mohrbach, arXiv:hep-th/0310167(2003) and arXiv:hep-th/0404165(2004)
18. A. P. Balachandran, T. R. Govindarajan, C. Molina, and P. Teotonio-Sobrinho, arXiv:hep-th/0406125, (2004).
19. P. A. Horváthy and M. S. Plyushchay, Phys. Lett. B 595, 547 (2004).
20. See e.g. [8]
21. Well known in symplectic mechanics, see e.g.[5, 6, 9].
22. j are antisymmetric.
23. 0 = √m′k′ → |B|.
24. 2 variables.
25. The (N = 3) case wil only be examined in the nondegenerate case χ > 0.
26. 2 + 2KK′ rCeB=1, the mass and elastic constant of the z degrees of freedom, as expected, are not renormalised.
27. αβ} in *(SO(N)}.
28. Exercise 4.2A in [6], defining a (generalized) Poincaré momentum.
29. 2 and on general noncommutative Riemann surfaces was examined in ([12, 13].
30. In the case e = 0, Darboux coordinates are given by (111.17) and in [16] such model was considered with the possibility of having a monopole in p-space!
31. f.
32. tX d on differential forms.
33. 1 is the primary constrained manifold, arising e.g. from a degenerate Lagrangian.