Fibre bundle formulation of nonrelativistic quantum mechanics: I. Introduction. The evolution transport

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dc.creatorIliev, Bozhidar Z.
dc.date1998-03-29
dc.date1998-10-16
dc.date.accessioned2026-07-07T10:55:04Z
dc.date.available2026-07-07T10:55:04Z
dc.descriptionWe 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. Its evolution is determined through the bundle (analogue of the) Schrödinger 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 first part of this investigation is devoted to the introduction of basic concepts on which the fibre bundle approach to quantum mechanics rests. We show that the evolution of pure quantum-mechanical states can be described as a suitable linear transport along paths, called evolution transport, of the state sections in the Hilbert fibre bundle of states of a considered quantum system.
dc.description26 standard (11pt, A4) LaTeX 2e pages. The packages AMS-LaTeX and amsfonts are required. Revised: new material, references, and comments are added. Minor style chages. Continuation of quan-ph/9803083. For continuation of the this series see http://www.inrne.bas.bg/mathmod/bozhome/
dc.identifierhttps://arxiv.org/abs/quant-ph/9803084
dc.identifierhttp://arxiv.org/abs/quant-ph/9803084
dc.identifierJ.Phys.A34:4887-4918,2001
dc.identifierdoi:10.1088/0305-4470/34/23/308
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/186001
dc.subjectQuantum Physics
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectHigh Energy Physics - Theory
dc.subjectDifferential Geometry
dc.subjectGeometric Topology
dc.titleFibre bundle formulation of nonrelativistic quantum mechanics: I. Introduction. The evolution transport
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