dorsal/arxiv
View SchemaQuantum Magnetic Algebra and Magnetic Curvature
| Authors | M. V. Karasev, T. A. Osborn |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0311053 |
| URL | https://arxiv.org/abs/quant-ph/0311053 |
| DOI | 10.1088/0305-4470/37/6/025 |
| Journal | J. Phys. A: Math. Gen. 37 (2004) 2345-2363 |
Abstract
The symplectic geometry of the phase space associated with a charged particle is determined by the addition of the Faraday 2-form to the standard structure on the Euclidean phase space. In this paper we describe the corresponding algebra of Weyl-symmetrized functions in coordinate and momentum operators satisfying nonlinear commutation relations. The multiplication in this algebra generates an associative product of functions on the phase space. This product is given by an integral kernel whose phase is the symplectic area of a groupoid-consistent membrane. A symplectic phase space connection with non-trivial curvature is extracted from the magnetic reflections associated with the Stratonovich quantizer. Zero and constant curvature cases are considered as examples. The quantization with both static and time dependent electromagnetic fields is obtained. The expansion of the product by the deformation parameter, written in the covariant form, is compared with the known deformation quantization formulas.
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"abstract": "The symplectic geometry of the phase space associated with a charged particle\nis determined by the addition of the Faraday 2-form to the standard structure\non the Euclidean phase space. In this paper we describe the corresponding\nalgebra of Weyl-symmetrized functions in coordinate and momentum operators\nsatisfying nonlinear commutation relations. The multiplication in this algebra\ngenerates an associative product of functions on the phase space. This product\nis given by an integral kernel whose phase is the symplectic area of a\ngroupoid-consistent membrane. A symplectic phase space connection with\nnon-trivial curvature is extracted from the magnetic reflections associated\nwith the Stratonovich quantizer. Zero and constant curvature cases are\nconsidered as examples. The quantization with both static and time dependent\nelectromagnetic fields is obtained. The expansion of the product by the\ndeformation parameter, written in the covariant form, is compared with the\nknown deformation quantization formulas.",
"arxiv_id": "quant-ph/0311053",
"authors": [
"M. V. Karasev",
"T. A. Osborn"
],
"categories": [
"quant-ph",
"math-ph",
"math.MP",
"math.SG"
],
"doi": "10.1088/0305-4470/37/6/025",
"journal_ref": "J. Phys. A: Math. Gen. 37 (2004) 2345-2363",
"title": "Quantum Magnetic Algebra and Magnetic Curvature",
"url": "https://arxiv.org/abs/quant-ph/0311053"
},
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