Physics – Mathematical Physics
Scientific paper
2009-04-22
Int. J.Mod. Phys. A, Vol: 24 (Issue: 24), 4573-4587, (2009).
Physics
Mathematical Physics
15 pages, no figures. Accepted for publication in Int. J. Mod. Phys. A
Scientific paper
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 linear-nonlinear canonical transformations and intertwining method can be treated within this argument.
Dereli Tekin
Hakioglu Tugrul
Tegmen Adnan
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