  The effects of a nonsimply connected spacetime with the topology of
$S^{1}\times R^{3}$ in the vacua of QED and gauged-NJL theories are
investigated. It is shown that the polarization effects of twisted and
untwisted fermions in QED are equivalent, once the corresponding stable vacuum
solution of each fermion class is taken into account. The photon propagation in
QED is found to be anisotropic and characterized by several massive photon
modes and a superluminal transverse mode. At small compactification radius the
masses of the massive modes increase as the inverse of the radius, while the
massless photon mode has a superluminal velocity that increases logarithmically
with that distance. At low energies the photon masses lead to an effective
confinement of the gauge fields into a $(2+1)-$dimensional manifold transverse
to the compactified direction. In the gauged-NJL model, it is shown that for
both twisted and untwisted fermions, the smaller the compactification radius,
the larger the critical four-fermion coupling needed to generate a
fermion-antifermion chiral symmetry breaking condensate.
