Positive and Negative Charges in Relativistic Schroedinger Theory

TL;DR

Relativistic Schroedinger Theory (RST) provides a consistent gauge framework for describing systems with positive and negative charges, explaining exchange effects for identical particles through gauge symmetry reduction rather than antisymmetrization.

Contribution

RST introduces a gauge-theoretic foundation for charge interactions and exchange effects, differing from conventional antisymmetrization approaches.

Findings

RST accounts for electromagnetic and exchange interactions among identical particles.

The gauge symmetry reduction explains the origin of exchange effects.

Demonstrated with a three-particle system involving electrons and a positive charge.

Abstract

Relativistic Schroedinger Theory (RST), as a general gauge theory for the description of relativistic N-particle systems, is shown to be a mathematically consistent and physically reasonable framework for an arbitrary assemblage of positive and negative charges. The electromagnetic plus exchange interactions within the subset of {\it identical} particles are accounted for in a consistent way, whereas {\it different} particles can undergo only the electromagnetic interactions. The origin of this different interaction mechanism for the subsets of identical and non-identical particles is traced back to the fundamental conservation laws for charge and energy-momentum: in order that these conservation laws can hold also for different particles, the structure group $\mathcal U(N)$ of the fibre bundles must be reduced to its maximal Abelian subgroup $\mathcal U(1) \times \mathcal U(1) \times ... \times \mathcal U(1)$, which eliminates the exchange part of the bundle connection. The persisting Abelian gauge symmetry adopts the meaning of the proper gauge group for the electromagnetic interactions which apply to the identical and non-identical particles in the same way. Thus in RST there is an intrinsic dynamical foundation of the emergence of exchange effects for identical particles, whereas the conventional theory is invaded by the exchange phenomenon via a purely kinematical postulate, namely the antisymmetrization postulate for the wave functions due to Pauli's exclusion principle. As a concrete demonstration, a three-particle system is considered which consists of a positively charged particle of arbitrary rest mass and of two negatively charged particles of equal spin, mass and charge (e.g. electrons).