Group theory and quasiprobability integrals of Wigner functions

Journal of Physics A: Mathematical and General

Volumn 36, Issue 20, 2003, Pages

  Bracken, Anthony J ^a,b   Ellinas, Demosthenes ^b   Wood, James G ^a  

^a UNIVERSITY OF QUEENSLAND   (Australia)

^b TECHNICAL UNIVERSITY OF CRETE   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037501407     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/36/20/102     Document Type: Article

References (17)

1. Wigner E P 1932 On the quantum correction for thermodynamic equilibrium Phys. Rev. 40 749-59
2. Bracken A J, Doebner H-D and Wood J G 1999 Bounds on integrals of the Wigner function Phys. Rev. Lett. 83 3758-61
3. Bracken A J, Ellinas D and Wood J G Non-positivity of the Wigner function and bounds on associated integrals Proc. Wigner Centennial Conf. (Pécs, Hungary, 2002) Acta. Phys. Hung. at press
4. Leonhardt U 1997 Measuring the Quantum State of Light (Cambridge: Cambridge University Press)
5. Schleich W P and Raymer M G (ed) 1997 Quantum state preparation and measurement J. Mod. Opt. 44 12
6. Abramowitz M and Stegun I A 1972 Handbook of Mathematical Functions (New York: Dover)
7. Croenewold H 1946 On the principles of elementary quantum mechanics Physica 12 405-60
8. Moyal J E 1949 Quantum mechanics as a statistical theory Proc. Camb. Phil. Soc. 45 99-124
9. Vilenkin N J and Klimyk A U 1991 Representations of Lie Groups and Special Functions vol I (Dordrecht: Kluwer)
10. Floreanini R, LeTourneux J and Vinet L 1993 Quantum mechanics and polynomials of a discrete variable Ann. Phys., NY 226 331-49
11. q(su(1, 1)) and generating functions for orthogonal polynomials J. Math. Phys. 39 5062-78
12. Nikiforov A F, Duslov S K and Uvarov V B 1991 Classical Orthogonal Polynomials of a Discrete Variable (Berlin: Springer)
13. Van der Jeugt J 1997 Coupling coefficients for Lie algebra representations and addition formulas for special functions J. Math. Phys. 38 2728-40
14. Koelink H T and Van der Jeugt J 1998 Convolutions for orthogonal polynomials from Lie and quantum algebra representations SIAM J. Math. Anal. 29 794-822
15. Bacry H. 1990 A unitary representation of SL(2, R) J. Math. Phys. 31 2061-77
16. Gilmore R 1974 Lie Groups and Some of their Applications (New York: Wiley)
17. Lahti P and Pellonpää J-P 1999 Covariant phase observables in quantum mechanics J. Math. Phys. 40 4688-98