Abstract
We study construction of the star-product version of three basic quantum canonical transformations which are known as the generators of the full canonical algebra. By considering the fact that star-product of c-number phase-space functions is in complete isomorphism to Hilbert-space operator algebra, it is shown that while the constructions of gauge and point transformations are immediate, generator of the interchanging transformation deforms this isomorphism. As an alternative approach, we study all of them within the deformed form. How to transform any c-number function under linear-nonlinear transformations and the intertwining method are shown within this argument as the complementary subjects of the text.
Highlights
In this work, we construct quantum canonical transformations (QCTs) in phase-space formalism developed by H
Canonical transformations in Moyal formalism revisited According to the definition of a CT in the star-product formalism, the interchange transformation must be in the form
Consists of gauge, point and interchange again, where the generating function (GF) ℘ of the point transformation in the forth step is given by the equations i f (q) =
Summary
We construct quantum canonical transformations (QCTs) in phase-space formalism developed by H. We will say Moyal or starproduct formalism in short for this phase-space formalism. The same triplet in quantum mechanics may be used to generate the classical CTs but this point is out of the scope of this work.
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