Born–Jordan Pseudodifferential Calculus, Bopp Operators and Deformation Quantization

Abstract

There has recently been a resurgence of interest in Born–Jordan quantization, which historically preceded Weyl’s prescription. Both mathematicians and physicists have found that this forgotten quantization scheme is actually not only of great mathematical interest, but also has unexpected application in operator theory, signal processing, and time-frequency analysis. In the present paper we discuss the applications to deformation quantization, which in its traditional form relies on Weyl quantization. Introducing the notion of “Bopp operator” which we have used in previous work, this allows us to obtain interesting new results in the spectral theory of deformation quantization.