Complex numbers and symmetries in quantum mechanics, and a nonlinear superposition principle for wigner functions

Reports on Mathematical Physics

Volumn 57, Issue 1, 2006, Pages 17-26

  Bracken, A J ^a  

^a UNIVERSITY OF QUEENSLAND   (Australia)

Author keywords

complex quantum mechanics; nonlinear superposition principle; quantum mechanics in phase space; quantum symmetries; Wigner functions

Indexed keywords

EID: 33744532287     PISSN: 00344877     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0034-4877(06)80005-4     Document Type: Article

References (23)

1. Feynman R.P. The Theory of Fundamental Processes (1962), Benjamin Cummings, Reading, Massachusetts
2. Dirac P.A.M. Fields and Quanta 3 (1972) 139
3. Moore W.J. Schrödinger: Life and Thought (1989), Cambridge University Press, Cambridge
4. Groenewold H. Physica 12 (1946) 405
5. Moyal J.E. Proc. Camb. Phil. Soc. 45 (1949) 99
6. Dubin D.A., Hennings M.A., and Smith T.B. Mathematical Aspects of Weyl Quantization and Phase (2000), World Scientific, Singapore
7. Berry M.V. Phil. Trans. R. Soc. A 287 (1977) 237
8. Leonhardt U. Measuring the Quantum State of Light (1997), Cambridge University Press, Cambridge
9. Bracken A.J., Doebner H.-D., and Wood J.G. Phys. Rev. Lett. 83 (1999) 3758
10. Osborn T.A., and Molzahn F.H. Annals Phys. 241 (1995) 79
11. Bracken A.J. J. Phys. A: Math. Gen. 36 (2003) L329
12. Bayen F., Flato M., Fronsdal C., Lichnerowicz A., and Sternheimer D. Annals Phys. 111 (1978) 61
13. Bayen F., Flato M., Fronsdal C., Lichnerowicz A., and Sternheimer D. Annals Phys. 111 (1978) 111
14. Fronsdal C. Rep. Math. Phys. 15 (1978) 111
15. Zachos C.K. Int. J. Mod. Phys. A 17 (2002) 297
16. Wigner E.P. Group Theory and its Applications to the Quantum Mechanics of Atomic Spectra (1956), Academic Press, New York
17. Bargmann V. J. Math. Phys. 5 (1964) 862
18. Cassinelli G., de Vito E., Lahti P.J., and Levrero A. Rev. Math. Phys. 9 (1997) 921
19. Bracken A.J., Cassinelli G., and Wood J.G. J. Phys. A: Math. Gen. 36 (2003) 1033
20. Tatarskii V. Sov. Phys. Usp. 26 (1983) 311
21. Takabayasi T. Prog. Theor. Phys. 11 (1954) 341
22. Fano U. Rev. Mod. Phys. 29 (1957) 74
23. Dias N.C., and Prata J.N. Annals Phys. 313 (2004) 110