Torus as phase space: Weyl quantization, dequantization, and Wigner formalism

2016/08/01 by Marilena Ligabò · 18 citations
Computer Science · Mathematics · Physics and Astronomy · #Canonical quantization #Formalism (music) #Geometric quantization #Geometry #Heisenberg picture #Mathematical physics #Mathematics #Method of quantum characteristics #Nonlinear Dynamics and Pattern Formation #Observable #Pauli matrices #Phase space #Physics #Pure mathematics #Quantization (signal processing) #Quantum #Quantum Mechanics and Applications #Quantum chaos #Quantum chaos and dynamical systems #Quantum dynamics #Quantum gravity #Quantum mechanics #Torus

paper · doi:10.1063/1.4961325

published in Journal of Mathematical Physics 57(8) (American Institute of Physics)

openalex publication_date 2016/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21

Abstract

The Weyl quantization of classical observables on the torus (as phase space) without regularity assumptions is explicitly computed. The equivalence class of symbols yielding the same Weyl operator is characterized. The Heisenberg equation for the dynamics of general quantum observables is written through the Moyal brackets on the torus and the support of the Wigner transform is characterized. Finally, a dequantization procedure is introduced that applies, for instance, to the Pauli matrices. As a result we obtain the corresponding classical symbols.

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• Modeling Position and Momentum in Finite-Dimensional Hilbert Spaces via Generalized Pauli Operators
• Comments on the Weyl-Wigner calculus for lattice models
• A Gutzwiller trace formula for large hermitian matrices

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