Bopp Pseudo-differential Operators

Part of the Pseudo-Differential Operators book series (PDO, volume 7)


Bopp pseudo-differential operators are the operators formally obtained from a symbol by the quantization rules
$$x \to x + \frac{1} {2}i\rlap{--} h\partial _{p\,} \,,\,\,p \to p - \frac{1} {2}i\rlap{--} h\partial _x$$
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.


Deformation Quantization Partial Isometry Quantization Rule Weyl Operator Phase Space Function 


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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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