dorsal/arxiv
View SchemaTopology Classes of Flat U(1) Bundles and Diffeomorphic Covariant Representations of the Heisenberg Algebra
| Authors | Jan Govaerts, Victor M. Villanueva |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9908014 |
| URL | https://arxiv.org/abs/quant-ph/9908014 |
| DOI | 10.1142/S0217751X00002846 |
| Journal | Int.J.Mod.Phys. A15 (2000) 4903-4932 |
Abstract
The general construction of self-adjoint configuration space representations of the Heisenberg algebra over an arbitrary manifold is considered. All such inequivalent representations are parametrised in terms of the topology classes of flat U(1) bundles over the configuration space manifold. In the case of Riemannian manifolds, these representations are also manifestly diffeomorphic covariant. The general discussion, illustrated by some simple examples in non relativistic quantum mechanics, is of particular relevance to systems whose configuration space is parametrised by curvilinear coordinates or is not simply connected, which thus include for instance the modular spaces of theories of non abelian gauge fields and gravity.
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"abstract": "The general construction of self-adjoint configuration space representations\nof the Heisenberg algebra over an arbitrary manifold is considered. All such\ninequivalent representations are parametrised in terms of the topology classes\nof flat U(1) bundles over the configuration space manifold. In the case of\nRiemannian manifolds, these representations are also manifestly diffeomorphic\ncovariant. The general discussion, illustrated by some simple examples in non\nrelativistic quantum mechanics, is of particular relevance to systems whose\nconfiguration space is parametrised by curvilinear coordinates or is not simply\nconnected, which thus include for instance the modular spaces of theories of\nnon abelian gauge fields and gravity.",
"arxiv_id": "quant-ph/9908014",
"authors": [
"Jan Govaerts",
"Victor M. Villanueva"
],
"categories": [
"quant-ph",
"hep-th",
"math-ph",
"math.MP"
],
"doi": "10.1142/S0217751X00002846",
"journal_ref": "Int.J.Mod.Phys. A15 (2000) 4903-4932",
"title": "Topology Classes of Flat U(1) Bundles and Diffeomorphic Covariant Representations of the Heisenberg Algebra",
"url": "https://arxiv.org/abs/quant-ph/9908014"
},
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