  In this paper we study the effects associated to quantum vacuum fluctuations
of vectorial perturbations of the Abelian SU(2) Yang-Mills field in a static
and homogeneous chromomagnetic-like background field, at zero temperature. We
use periodic and antiperiodic boundary conditions in order to calculate the
Casimir energy by means of the frequency sum technique and of the
regularization method based on zeta functions, analyzing its behavior in the
weak and strong coupling regimes. We compare the obtained results with the
similar ones found for scalar and spinor fields placed in an ordinary magnetic
field background. We show that only in the weak coupling regime the non-trivial
topology of the system encoded in the antiperiodic boundary conditions changes
the nature of the Casimir force with respect to the periodic ones. Considering
the weak coupling scenario, we show that the introduction of a third
polarization state in the perturbations makes manifest the effects on the
Casimir energy due to the coupling with the chromomagnetic-like background
field, for both the boundary conditions. Finally, in the strong coupling
regime, in which the quantum vacuum is not stable due to the Nielsen-Olesen
instabilities, we evaluate the effects of a compact extra dimension on its
stabilization.
