dorsal/arxiv
View SchemaQuantum Mechanics in Multiply-Connected Spaces
| Authors | Detlef Duerr, Sheldon Goldstein, James Taylor, Roderich Tumulka, Nino Zanghi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0506173 |
| URL | https://arxiv.org/abs/quant-ph/0506173 |
| DOI | 10.1088/1751-8113/40/12/S08 |
| Journal | J. Phys. A: Math. Theor. 40 (2007) 2997-3031 |
Abstract
We explain why, in a configuration space that is multiply connected, i.e., whose fundamental group is nontrivial, there are several quantum theories, corresponding to different choices of topological factors. We do this in the context of Bohmian mechanics, a quantum theory without observers from which the quantum formalism can be derived. What we do can be regarded as generalizing the Bohmian dynamics on $\mathbb{R}^{3N}$ to arbitrary Riemannian manifolds, and classifying the possible dynamics that arise. This approach provides a new understanding of the topological features of quantum theory, such as the symmetrization postulate for identical particles. For our analysis we employ wave functions on the universal covering space of the configuration space.
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"abstract": "We explain why, in a configuration space that is multiply connected, i.e.,\nwhose fundamental group is nontrivial, there are several quantum theories,\ncorresponding to different choices of topological factors. We do this in the\ncontext of Bohmian mechanics, a quantum theory without observers from which the\nquantum formalism can be derived. What we do can be regarded as generalizing\nthe Bohmian dynamics on $\\mathbb{R}^{3N}$ to arbitrary Riemannian manifolds,\nand classifying the possible dynamics that arise. This approach provides a new\nunderstanding of the topological features of quantum theory, such as the\nsymmetrization postulate for identical particles. For our analysis we employ\nwave functions on the universal covering space of the configuration space.",
"arxiv_id": "quant-ph/0506173",
"authors": [
"Detlef Duerr",
"Sheldon Goldstein",
"James Taylor",
"Roderich Tumulka",
"Nino Zanghi"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/1751-8113/40/12/S08",
"journal_ref": "J. Phys. A: Math. Theor. 40 (2007) 2997-3031",
"title": "Quantum Mechanics in Multiply-Connected Spaces",
"url": "https://arxiv.org/abs/quant-ph/0506173"
},
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