Work

Weyl–Heisenberg covariant quantization for the discrete torus

Year: 2025

Type: article

Abstract: Covariant integral quantization is implemented for systems whose phase space is [Formula: see text], i.e. for systems moving on the discrete periodic set [Formula: see text] mod [Formula: see text]. The symmetry group of this phase space is the periodic discrete version of the Weyl–Heisenberg group, namely the central extension of the abelian group [Formula: see text]. In this regard, the phase space is viewed as the left coset of the group with its center. The non-trivial unitary irreducible representation of this group, as acting on [Formula: see text], is square integrable on the phase We derive the corresponding covariant integral quantizations from (weight) functions on the phase space, and display their phase space portrait.

Source: International Journal of Geometric Methods in Modern Physics

DOI: 10.1142/s0219887825400341

Authors: Romain Murenzi, Aidan Zlotak, Jean-Pierre Gazeau

Institutions: Worcester Polytechnic Institute, Centre National de la Recherche Scientifique, Université Paris Cité, University of Białystok, Laboratoire AstroParticule et Cosmologie, Université Paris Diderot

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Worcester Polytechnic Institute

OpenAlex ID: W4405792677

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