English

Twisted Fourier analysis and pseudo-probability distributions

Mathematical Physics 2020-05-19 v3 Functional Analysis math.MP Operator Algebras Quantum Physics

Abstract

We use a noncommutative generalization of Fourier analysis to define a broad class of pseudo-probability representations, which includes the known bosonic and discrete Wigner functions. We characterize the groups of quantum unitary operations which correspond to phase-space transformations, generalizing Gaussian and Clifford operations. As examples, we find Wigner representations for fermions, hard-core bosons, and angle-number systems.

Keywords

Cite

@article{arxiv.2004.13860,
  title  = {Twisted Fourier analysis and pseudo-probability distributions},
  author = {Sang Jun Park and Cedric Beny and Hun Hee Lee},
  journal= {arXiv preprint arXiv:2004.13860},
  year   = {2020}
}

Comments

It has been specified that we are recovering Mukunda's Wigner function for angle-number system. There have been some typo corrections

R2 v1 2026-06-23T15:10:08.233Z