Fibre bundle formulation of relativistic quantum mechanics
Abstract
We propose a fibre bundle formulation of the mathematical base of relativistic quantum mechanics. At the present stage the bundle form of the theory is equivalent to its conventional one, but it admits new types of generalizations in different directions. In the bundle description the wavefunctions are replaced with (state) sections (covariant approach) or liftings of paths (equivalently: sections along paths) (time-dependent approach) of a suitably chosen vector bundle over space-time whose (standard) fibre is the space of the wavefunctions. Now the quantum evolution is described as a linear transportation of the state sections/liftings in the (total) bundle space. The equations of these transportations turn to be the bundle versions of the corresponding relativistic wave equations. Connections between the (retarded) Green functions of these equations and the evolution operators and transports are found. Especially the Dirac and Klein-Gordon equations are considered.
Cite
@article{arxiv.quant-ph/0201085,
title = {Fibre bundle formulation of relativistic quantum mechanics},
author = {Bozhidar Z. Iliev},
journal= {arXiv preprint arXiv:quant-ph/0201085},
year = {2007}
}
Comments
Essentially revised version in which an error in the previous one is corrected. 24 LaTeX 2e pages. The packages AMS-LaTeX and amsfonts are required. This is a unified and updated version of the papers quant-ph/0105056 and quant-ph/0107002. For related works, view the "publication" pages at http://theo.inrne.bas.bg/~bozho/