dorsal/arxiv
View SchemaThe Weyl representation on the torus
| Authors | A. M. F. Rivas, A. M. Ozorio de Almeida |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9904041 |
| URL | https://arxiv.org/abs/quant-ph/9904041 |
| DOI | 10.1006/aphy.1999.5942 |
| Journal | Annals Phys. 276 (1999) 223-256 |
Abstract
We construct reflection and translation operators on the Hilbert space corresponding to the torus by projecting them from the plane. These operators are shown to have the same group properties as their analogue on the plane. The decomposition of operators in the basis of reflections corresponds to the Weyl or center representation, conjugate to the chord representation which is based on quantized translations. Thus, the symbol of any operator on the torus is derived as the projection of the symbol on the plane. The group properties allow us to derive the product law for an arbitrary number of operators in a simple form. The analogy between the center and the chord representations on the torus to those on the plane is then exploited to treat Hamiltonian systems defined on the torus and to formulate a path integral representation of the evolution operator. We derive its semiclassical approximation.
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"abstract": "We construct reflection and translation operators on the Hilbert space\ncorresponding to the torus by projecting them from the plane. These operators\nare shown to have the same group properties as their analogue on the plane. The\ndecomposition of operators in the basis of reflections corresponds to the Weyl\nor center representation, conjugate to the chord representation which is based\non quantized translations. Thus, the symbol of any operator on the torus is\nderived as the projection of the symbol on the plane. The group properties\nallow us to derive the product law for an arbitrary number of operators in a\nsimple form. The analogy between the center and the chord representations on\nthe torus to those on the plane is then exploited to treat Hamiltonian systems\ndefined on the torus and to formulate a path integral representation of the\nevolution operator. We derive its semiclassical approximation.",
"arxiv_id": "quant-ph/9904041",
"authors": [
"A. M. F. Rivas",
"A. M. Ozorio de Almeida"
],
"categories": [
"quant-ph",
"chao-dyn",
"nlin.CD"
],
"doi": "10.1006/aphy.1999.5942",
"journal_ref": "Annals Phys. 276 (1999) 223-256",
"title": "The Weyl representation on the torus",
"url": "https://arxiv.org/abs/quant-ph/9904041"
},
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