Fibre bundle formulation of nonrelativistic quantum mechanics. 0. Preliminary considerations: Quantum mechanics from a geometric-observer's viewpoint

Abstract

We propose a version of the non-relativistic quantum mechanics in which the pure states of a quantum system are described as sections of a Hilbert (generally infinitely-dimensional) fibre bundle over the space-time. There evolution is governed via (a kind of) a parallel transport in this bundle. Some problems concerning observables are considered. There are derived the equations of motion for the state sections and observables. We show that up to a constant the matrix of the coefficients of the evolution operator (transport) coincides with the matrix of the Hamiltonian of the investigated quantum system.

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References in corpus (2)

• Transports along Paths in Fibre Bundles. III. Consistency with Bundle Morphisms
• Linear transports along paths in vector bundles V. Properties of curvature and torsion

Cited by in corpus (6)

• Fibre bundle formulation of nonrelativistic quantum mechanics: I. Introduction. The evolution transport
• Fibre bundle formulation of nonrelativistic quantum mechanics. II. Equations of motion and observables
• Fibre bundle formulation of nonrelativistic quantum mechanics (full version)
• Pseudo-forces in quantum mechanics
• Fibre bundle formulation of relativistic quantum mechanics
• Fibre bundle formulation of relativistic quantum mechanics. I. Time-dependent approach