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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pram/065/06/0981-0993

    • Keywords

       

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

    • Abstract

       

      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

    • Author Affiliations

       

      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

    • Dates

       
      Published
      December 2005
      Manuscript received
      11 July 2005
      Accepted
      20 August 2005

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