dorsal/arxiv
View SchemaFibre bundle formulation of nonrelativistic quantum mechanics. IV. Mixed states and evolution transport's curvature
| Authors | Bozhidar Z. Iliev |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9901039 |
| URL | https://arxiv.org/abs/quant-ph/9901039 |
| DOI | 10.1142/S0217751X02005669 |
| Journal | Int.J.Mod.Phys. A17 (2002) 229-243 |
Abstract
We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits new generalizations in different directions. In it a pure state of some quantum system is described by a state section (along paths) of a (Hilbert) fibre bundle. It's evolution is determined through the bundle (analogue of the) Schr\"odinger equation. Now the dynamical variables and the density operator are described via bundle morphisms (along paths). The mentioned quantities are connected by a number of relations derived in this work. The present fourth part of this series is devoted mainly to the fibre bundle description of mixed quantum states. We show that to the conventional density operator there corresponds a unique density morphism (along paths) for which the corresponding equations of motion are derived. It is also investigated the bundle description of mixed quantum states in the different pictures of motion. We calculate the curvature of the evolution transport and prove that it is curvature free iff the values of the Hamiltonian operator at different moments commute.
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"abstract": "We propose a new systematic fibre bundle formulation of nonrelativistic\nquantum mechanics. The new form of the theory is equivalent to the usual one\nbut it is in harmony with the modern trends in theoretical physics and\npotentially admits new generalizations in different directions. In it a pure\nstate of some quantum system is described by a state section (along paths) of a\n(Hilbert) fibre bundle. It\u0027s evolution is determined through the bundle\n(analogue of the) Schr\\\"odinger equation. Now the dynamical variables and the\ndensity operator are described via bundle morphisms (along paths). The\nmentioned quantities are connected by a number of relations derived in this\nwork.\n The present fourth part of this series is devoted mainly to the fibre bundle\ndescription of mixed quantum states. We show that to the conventional density\noperator there corresponds a unique density morphism (along paths) for which\nthe corresponding equations of motion are derived. It is also investigated the\nbundle description of mixed quantum states in the different pictures of motion.\nWe calculate the curvature of the evolution transport and prove that it is\ncurvature free iff the values of the Hamiltonian operator at different moments\ncommute.",
"arxiv_id": "quant-ph/9901039",
"authors": [
"Bozhidar Z. Iliev"
],
"categories": [
"quant-ph",
"hep-th"
],
"doi": "10.1142/S0217751X02005669",
"journal_ref": "Int.J.Mod.Phys. A17 (2002) 229-243",
"title": "Fibre bundle formulation of nonrelativistic quantum mechanics. IV. Mixed states and evolution transport\u0027s curvature",
"url": "https://arxiv.org/abs/quant-ph/9901039"
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