Fibre bundle formulation of relativistic quantum mechanics. II. Covariant approach
Abstract
Description
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 present, second, part of our investigation, we consider a covariant approach to bundle description of relativistic quantum mechanics.
In it the wavefunctions are replaced with (state) sections 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 (by means of the transport along the identity map of the space\nobreakdash-time) of the state sections in the (total) bundle space. Connections between the (retarded) Green functions of the relativistic wave equations and the evolution operators and transports are found. Especially the Dirac and Klein-Gordon equations are considered.
Essentially revised version in which an error in the previous one is corrected 18 standard LaTeX pages. The packages AMS-LaTeX and amsfonts are required. This paper is continuation of the E-print quant-ph/0105056. For related works, view the "publication" pages at http://theo.inrne.bas.bg/~bozho/
Essentially revised version in which an error in the previous one is corrected 18 standard LaTeX pages. The packages AMS-LaTeX and amsfonts are required. This paper is continuation of the E-print quant-ph/0105056. For related works, view the "publication" pages at http://theo.inrne.bas.bg/~bozho/