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Bopp Pseudo-differential Operators

  • Maurice A. de Gosson
Chapter
Part of the Pseudo-Differential Operators book series (PDO, volume 7)

Abstract

Bopp pseudo-differential operators are the operators formally obtained from a symbol by the quantization rules
$$x \to x + \frac{1} {2}i\rlap{--} h\partial _{p\,} \,,\,\,p \to p - \frac{1} {2}i\rlap{--} h\partial _x$$
(18.1)
instead of the usual correspondence\(x \to x,\,p\, \to \, - i\rlap{--} h\partial _{x.}\) The terminology comes from the fact that the operators \( x + \frac{1} {2}i\rlap{--} h\partial _{p\,} \,\text{and}\,\,\text{p} - \frac{\text{1}} {\text{2}}\,i\rlap{--} h\partial _x \) are called “Bopp shifts” in the physics literature.

Keywords

Deformation Quantization Partial Isometry Quantization Rule Weyl Operator Phase Space Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Faculty of Mathematics, NuHAGUniversity of ViennaViennaAustria

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