Lie group representations and quantization

Reports on Mathematical Physics

Volumn 47, Issue 2, 2001, Pages 213-240

  Aldaya, V ^a,b   Guerrero, J ^a,b,c  

^a INSTITUTO DE ASTROFÍSICA DE ANDALUCÍA CSIC   (Spain)

^b UNIVERSITY OF GRANADA   (Spain)

^c INFN SEZIONE DI NAPOLI   (Italy)

Author keywords

Anomalies; Coadjoint orbits; Group cohomology; Lie groups; Representations

Indexed keywords

EID: 0041368575     PISSN: 00344877     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0034-4877(01)80038-0     Document Type: Article

References (42)

1. Lévy-Leblond J.M. Loebl E.M. Group Theory and its Applications. 2:1971;Academic Press, New York.
2. Sudarshan E.C.G., Mukunda. Classical Dynamics: A Modern Perspective. 1974;Wiley, New York.
3. Aldaya V., de Azcárraga J. J. Math. Phys. 23:1982;1297.
4. Aldaya V., Guerrero J., Marmo G. Quantization on Lie Groups. Proceedings of the International Symposium Symmetries and Science X 1997. 1998;1-36 Plenum Press Corporation, New York and London.
5. Aldaya V., Navarro-Salas J., Bisquert J., Loll R. J. Math. Phys. 33:1992;3087.
6. Barut A.O., Ra̧czka R. Theory of Group Representations and Applications. 1986;World Scientific, Singapore.
7. J. Guerrero and V. Aldaya: Invariant measures on polarized submanifolds in group quantization, math-ph/0003024.
8. Aldaya V., Navarro-Salas J., Ramírez A. Commun. Math. Phys. 121:1989;541.
9. Bargmann V. Ann. Math. 59:1954;1.
10. Jacobson N. Lie Algebras. 1979;Dover Publications Inc. New York.
11. Souriau J.M. Structure des Systèmes Dynamiques. 1970;. Dunod.
12. Aldaya V., Bisquert J., Guerrero J., Navarro-Salas J. J. Phys. A 26:1993;5375.
13. Mickelsson J. Current Algebras and Groups. Plenum Monographs in Nonlinear Physics. 1989;Plenum, New York.
14. Mickelsson J. Phys. Rev. Lett. 55:1985;2099.
15. Pressley A., Segal G. Loop Groups. 1986;Clarendon Press, Oxford.
16. Pontrjaguin L.S. Topological Groups. 1939;Princeton.
17. Kirillov A.A. Elements of the Theory of Representations. 1976;Springer, Berlin.
18. Saletan E.J. J. Math. Phys. 2:1961;1.
19. Aldaya V., de Azcárraga J.A. Int. J. Theo. Phys. 24:1985;141.
20. Aldaya V., Navarro-Salas J. Commun. Math. Phys. 113:1987;375.
21. Aldaya V., Navarro-Salas J. Commun. Math. Phys. 139:1991;433.
22. Balachandran A.P., Marmo G., Skgerstam B.S., Stern A. Classical Topology and Quantum States. 1991;World Scientific, Singapore.
23. Woodhouse N. Geometric Quantization. 1980;Clarendon, Oxford.
24. Gel'fand I.M., Raikov D.A., Chilov G.E. Les Anneaux normis commutatifs. 1964;Gauthier-Villars, Paris.
25. Aldaya V., Guerrero J., Marmo G. Int. J. Mod. Phys. A. 12:1997;3-11.
26. Levi-Civita T., Amaldi U. Lezioni di Meccanica Razionale. 1974;Zanichelli, Bologna. (reprinted version of 1949 edition).
27. Aldaya V., Gotay M.J., Guerrero J. Commun. Math. Phys. 178:1996;399.
28. Fernández M., Gotay M.J., Gray A. Proc. Am. Math. Soc. 103:1988;1209.
29. Niederer U. Helv. Phys. Acta. 45:1972;802.
30. Niederer U. Helv. Phys. Acta. 46:1973;191.
31. Niederer U. Helv. Phys. Acta. 47:1974;167.
32. van Hove J. Acad. R. Belg., Cl. Sci., Mem., Collect. 6:1951;. t. XXVI.
33. Witten E. Commun. Math. Phys. 114:1988;1.
34. Streater R.F. Comm. Math. Phys. 4:1967;217.
35. Aldaya V., de Azcarraga J.A., Wolf K.B. J. Math. Phys. 25:1984;506.
36. Aldaya V., Guerrero J. J. Phys. A 28:1995;L137.
37. Aldaya V., Bisquert J., Guerrero J., Navarro-Salas J. Rep. Math. Phys. 37:1996;387.
38. Aldaya V., Calixto M., Guerrero J. Int. J. Mod. Phys. A13:1998;4889.
39. Yuen H.P. Phys. Rev. A 13:1976;2226.
40. Kac V.G. Lecture Notes in Physics. 94:1982;441 Springer, Berlin, Heidelberg, New York.
41. Sugawara H. Phys. Rev. 170:1968;1659.
42. Humphreys J.E. Introduction to Lie Algebras and Representation Theory. 1972;Springer, New York. Graduate Text in Mathematics.