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Torus as phase space: Weyl quantization, dequantization, and Wigner formalism. (English) Zbl 1351.81066
Author’s 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.

MSC:
81S30 Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
81S10 Geometry and quantization, symplectic methods
53D55 Deformation quantization, star products
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