Browsing by Subject "Canonical transformations"
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Item Open Access Canonical transformations in three-dimensional phase-space(2009) Dereli, T.; Teǧmen, A.; Hakioǧlu T.Canonical transformation in a three-dimensional phase-space endowed with Nambu bracket is discussed in a general framework. Definition of the canonical transformations is constructed based on canonoid transformations. It is shown that generating functions, transformed Hamilton functions and the transformation itself for given generating functions can be determined by solving Pfaffian differential equations corresponding to that quantities. Types of the generating functions are introduced and all of them are listed. Infinitesimal canonical transformations are also discussed. Finally, we show that the decomposition of canonical transformations is also possible in three-dimensional phase space as in the usual two-dimensional one. © 2009 World Scientific Publishing Company.Item Open Access Quantum canonical transformations in Weyl-Wigner-Groenewold-Moyal formalism(2009) Dereli, T.; Hakioğlu, T.; Teğmen, A.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.