Fibre bundle formulation of relativistic quantum mechanics. I. Time-dependent approach

摘要

We propose a new fibre bundle formulation of the mathematical base ofrelativistic quantum mechanics. At the present stage the bundle form of thetheory is equivalent to its conventional one, but it admits new types ofgeneralizations in different directions. In the present first part of our investigation we consider the time-dependentor Hamiltonian approach to bundle description of relativistic quantummechanics. In it the wavefunctions are replaced by (state) liftings of paths orsections along paths of a suitably chosen vector bundle over space-time whose(standard) fibre is the space of the wavefunctions. Now the quantum evolutionis described as a linear transportation (by means of the evolution transportalong paths in the space-time) of the state liftings/sections in the (total)bundle space. The equations of these transportations turn to be the bundleversions of the corresponding relativistic wave equations.