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      Quantum canonical transformations in Weyl-Wigner-Groenewold-Moyal formalism

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      Author(s)
      Dereli, T.
      Hakioğlu, T.
      Teğmen, A.
      Date
      2009
      Source Title
      International Journal of Modern Physics A
      Print ISSN
      0217-751X
      Volume
      24
      Issue
      24
      Pages
      4573 - 4587
      Language
      English
      Type
      Article
      Item Usage Stats
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      Abstract
      A conjecture in quantum mechanics states that any quantum canonical transformation can decompose into a sequence of three basic canonical transformations; gauge, point and interchange of coordinates and momenta. It is shown that if one attempts to construct the three basic transformations in star-product form, while gauge and point transformations are immediate in star-exponential form, interchange has no correspondent, but it is possible in an ordinary exponential form. As an alternative approach, it is shown that all three basic transformations can be constructed in the ordinary exponential form and that in some cases this approach provides more useful tools than the star-exponential form in finding the generating function for given canonical transformation or vice versa. It is also shown that transforms of c-number phase space functions under linearnonlinear canonical transformations and intertwining method can be treated within this argument. © 2009 World Scientific Publishing Company.
      Keywords
      Canonical transformations
      Moyal product
      Permalink
      http://hdl.handle.net/11693/22615
      Published Version (Please cite this version)
      http://dx.doi.org/10.1142/S0217751X09044620
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