  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.
