English

Weyl-Heisenberg integral quantization(s): a compendium

Quantum Physics 2017-03-27 v1 Mathematical Physics math.MP

Abstract

We present a list of formulae useful for Weyl-Heisenberg integral quantizations, with arbitrary weight, of functions or distributions on the plane. Most of these formulae are known, others are original. The list encompasses particular cases like Weyl-Wigner quantization (constant weight) and coherent states (CS) or Berezin quantization (Gaussian weight). The formulae are given with implicit assumptions on their validity on appropriate space(s) of functions (or distributions). One of the aims of the document is to accompany a work in progress on Weyl-Heisenberg integral quantization of dynamics for the motion of a point particle on the line.

Keywords

Cite

@article{arxiv.1703.08443,
  title  = {Weyl-Heisenberg integral quantization(s): a compendium},
  author = {Hervé Bergeron and Evaldo M. F. Curado and Jean-Pierre Gazeau and Ligia M. C. S. Rodrigues},
  journal= {arXiv preprint arXiv:1703.08443},
  year   = {2017}
}

Comments

50 pages

R2 v1 2026-06-22T18:56:00.271Z