On the Interaction between Fermions via Massless Bosons and Massive Particles

TL;DR

This paper calculates the interaction energy between two fermions mediated by massless and massive particles, revealing Coulomb-like behavior and potential well formation, with results aligning well with experimental data such as for the deuteron.

Contribution

It introduces a Hamiltonian based on flux line coupling to analyze fermion interactions via massless and massive bosons, providing new analytical expressions.

Findings

Interaction energy via massless bosons resembles Coulomb energy.

Massive particles induce a potential well in the interaction energy.

Spin-spin interactions modulate the potential with a cosine factor.

Abstract

By using a Hamiltonian based on the coupling through flux lines, we have calculated the interaction energy between two fermions via massless bosons as well as via massive particles. In the case of interaction via massless bosons we obtain an equivalent expression for the Coulomb's energy on the form, where is the fine structure constant. In the case of the interaction via massive particles we obtain that the interaction energy contains a term building the potential well. Taking into account the spin-spin interaction of the nucleons, we show that this interaction modulates the interaction potential through a cosine factor. The obtained results are in good agreement with experimental data, for example, of deuteron.