Titlebook: Born-Jordan Quantization; Theory and Applicati Maurice A. de Gosson Book 2016 Springer International Publishing Switzerland 2016 Grossmann-

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Symplectic Covariance PropertiesGiven an operator . a natural question that arises is what happens to that operator when one makes a change of variables in the symbol ..

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Symbol Classes and Function SpacesIn this chapter we initiate the study of continuity properties for Born–Jordan operators. We will discuss the global symbol classes introduced by Shubin; they are “global” in the sense that they satisfy growth estimates with an equal weighting on the position and momentum variables.

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Book 2016tures of quantum mechanics are equivalent only if the Born–Jordan scheme is used. Thus, Born–Jordan quantization provides the only physically consistent quantization scheme, as opposed to the Weyl quantization commonly used by physicists. In this book we develop Born–Jordan quantization from an oper

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https://doi.org/10.1007/b138344d discuss some unexpected properties of these operators; for instance we will show that Born–Jordan quantization is not one-to-one: the zero operator is the quantization of infinitely many classical phase space functions. Another approach, based on Shubin’s theory of pseudo-differential operators, will be developed in the forthcoming chapters.

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Born–Jordan Quantizationd discuss some unexpected properties of these operators; for instance we will show that Born–Jordan quantization is not one-to-one: the zero operator is the quantization of infinitely many classical phase space functions. Another approach, based on Shubin’s theory of pseudo-differential operators, will be developed in the forthcoming chapters.

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Book 2016aches, in particular the Feynman-integral point of view. One important and intriguing feature of Born-Jordan quantization is that it is not one-to-one: there are infinitely many classical observables whose quantization is zero..

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The Cohen Classntinuity, and translation covariance). These quasi-distributions are obtained from the Wigner transform by convolving the latter with a suitable tempered distribution. The Cohen class is widely used in time-frequency analysis and is being rediscovered in quantum mechanics.

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