Exchange Interactions and Principle of Minimal Energy in Relativistic Schroedinger Theory

TL;DR

This paper extends the principle of minimal energy in Relativistic Schroedinger Theory to include identical particles and exchange interactions, demonstrating the theory's consistency for fermionic and bosonic states.

Contribution

It generalizes the variational principle in RST to account for exchange forces among identical particles, including both fermionic and bosonic states.

Findings

The theory accommodates exchange interactions leading to nonlinearities.

Validation of the variational principle for fermionic and bosonic states.

Demonstration of the consistency of RST with different quantum states.

Abstract

The principle of minimal energy, which has been set up in the preceding papers for systems of non-identical particles (e.g. positronium), is now generalized to include also identical particles. Since the latter kind of particles feels also the exchange forces (besides the usual electromagnetic forces), one has to deal with non-zero exchange potentials which render the theory nonlinear, according to the non-Abelian character of Relativistic Schroedinger Theory (RST). However, the present extension of the variational principle refers only to the linearized version of RST in order to keep the calculations sufficiently simple. It is also demonstrated that in RST the Dirac particles can occur in fermionic and bosonic quantum states; and the mathematical and physical consistency of the variational principle is validated for both types of states (concretely the fermionic hydrogen state 2p_3/2 and the bosonic positronium state 2^1P_1).