# Bopp Pseudo-differential Operators

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## Abstract

Bopp pseudo-differential operators are the operators formally obtained from a symbol by the quantization rules 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.

$$x \to x + \frac{1}
{2}i\rlap{--} h\partial _{p\,} \,,\,\,p \to p - \frac{1}
{2}i\rlap{--} h\partial _x$$

(18.1)

## 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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