Fermion inter-particle potentials in 5D and a dimensional restriction prescription to 4D

TL;DR

This paper explores how fermion inter-particle potentials derived from gauge theories differ when computed in five dimensions and then reduced to four, revealing new effects absent in direct four-dimensional calculations.

Contribution

It introduces a dimensional reduction prescription that uncovers pseudo-spin effects in 4D potentials derived from 5D models, highlighting novel physical phenomena.

Findings

Identification of pseudo-spin dependence in 4D potentials

Demonstration of new effects arising from 5D to 4D reduction

Comparison showing differences with direct 4D calculations

Abstract

This work sets out to compute and discuss effects of spin, velocity and dimensionality on inter-particle potentials systematically derived from gauge field-theoretic models. We investigate the interaction of fermionic particles by the exchange of a vector field in a parity-preserving description in five-dimensional $(5D)$ space-time. A particular dimensional reduction prescription is adopted $-$ reduction by dimensional restriction $-$ and special effects, like a pseudo-spin dependence, show up in four dimensions $(4D)$. What we refer to as pseudo-spin shall be duly explained. The main idea we try to convey is that the calculation of the potentials in $5D$ and the consequent reduction to $4D$ exhibits new effects that are not present if the potential is calculated in $4D$ after the action has been reduced.