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

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.
Comment: In this version, new comments and results have been added in Sections IV, V and Concluding Comments. To be published in Phys. Rev. D