dorsal/arxiv
View SchemaFibre bundle formulation of nonrelativistic quantum mechanics. V. Theory's interpretation, summary and discussion
| Authors | Bozhidar Z. Iliev |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9902068 |
| URL | https://arxiv.org/abs/quant-ph/9902068 |
| DOI | 10.1142/S0217751X02005712 |
| Journal | Int.J.Mod.Phys. A17 (2002) 245-258 |
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. This is the fifth closing part of our investigation. We briefly discuss the observer's role in the theory and different realizations of the space-time model used as a base space in the bundle approach to quantum mechanics. We point the exact conditions for the equivalence of Hilbert bundle and Hilbert space formulations of the theory. A comparison table between the both description of nonrelativistic quantum mechanics is presented. We discuss some principal moments of the Hilbert bundle description and show that it is more general than the Hilbert space one. Different directions for further research are pointed too.
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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 This is the fifth closing part of our investigation. We briefly discuss the\nobserver\u0027s role in the theory and different realizations of the space-time\nmodel used as a base space in the bundle approach to quantum mechanics. We\npoint the exact conditions for the equivalence of Hilbert bundle and Hilbert\nspace formulations of the theory. A comparison table between the both\ndescription of nonrelativistic quantum mechanics is presented. We discuss some\nprincipal moments of the Hilbert bundle description and show that it is more\ngeneral than the Hilbert space one. Different directions for further research\nare pointed too.",
"arxiv_id": "quant-ph/9902068",
"authors": [
"Bozhidar Z. Iliev"
],
"categories": [
"quant-ph",
"hep-th"
],
"doi": "10.1142/S0217751X02005712",
"journal_ref": "Int.J.Mod.Phys. A17 (2002) 245-258",
"title": "Fibre bundle formulation of nonrelativistic quantum mechanics. V. Theory\u0027s interpretation, summary and discussion",
"url": "https://arxiv.org/abs/quant-ph/9902068"
},
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