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Wigner distribution; phase space; finite groups; representation theory; phase point operators

We discuss questions pertaining to the definition of ‘momentum’, ‘momentum space’, ‘phase space’ and ‘Wigner distributions’; for finite dimensional quantum systems. For such systems, where traditional concepts of ‘momenta’ established for continuum situations offer little help, we propose a physically reasonable and mathematically tangible definition and use it for the purpose of setting up Wigner distributions in a purely algebraic manner. It is found that the point of view adopted here is limited to odd dimensional systems only. The mathematical reasons which force this situation are examined in detail

S Chaturvedi¹ E Ercolessi² G Marmo³ G Morandi⁴ N Mukunda⁵ R Simon⁶

1. School of Physics, University of Hyderabad, Hyderabad - 500 046, India
2. Physics Department, University of Bologna, INFM and INFN, Via Irnerio, Bologna - 46, I-40126, Italy
3. Dipartimento di Scienze Fisiche, University of Napoli and INFN, Via Cinzia, Napoli - I-80126, Italy
4. Physics Department, University of Bologna, INFM and INFN, V.le B.Pichat, Bologna - 6/2, I-40127, Italy
5. Centre for High Energy Physics, Indian Institute of Science, Bangalore - 560 012, India
6. The Institute of Mathematical Sciences, C.I.T. Campus, Chennai - 600 113, India

Published

December 2005

Manuscript received

11 July 2005

Accepted

20 August 2005