Deformation Quantization of the Heisenberg Group
F.Bonechi, R.Giachetti, E.Sorace, M.Tarlini (Dipartimento di, Fisica, Universita` di Firenze, INFN--Firenze, Dipartimento di Matematica,, Universita` di Bologna.)
TL;DR
This paper develops a deformation quantization of the Heisenberg group using a *-product aligned with its Hopf algebra structure, explicitly calculating the quantum group's R-matrix and exploring its properties.
Contribution
It introduces a new *-product compatible with the Hopf algebra structure of the Heisenberg group and explicitly computes the associated R-matrix.
Findings
Explicit *-product for the Heisenberg group derived
Quantum group structure analyzed with R-matrix calculation
Connection established between Lie-Poisson structures and quantum deformations
Abstract
A *-product compatible with the comultiplication of the Hopf algebra of the functions on the Heisenberg group is determined by deforming a coboundary Lie-Poisson structure defined by a classical r-matrix satisfying the modified Yang-Baxter equation. The corresponding quantum group is studied and its R-matrix is explicitly calculated.
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