  In this paper the effective potential approach in quantum field theory is
used in order to investigate self-interaction loop correction to the Casimir
energy density and generation of topological mass for both massless and massive
real scalar fields. It is assumed that the scalar field obeys a helix boundary
condition. In addition, it is also considered a CPT-even aether-type violation
of the Lorentz symmetry. In the absence of the Lorentz violation we obtain
analytical expressions for the loop correction to the Casimir energy density
and to the mass of the scalar field. The same expressions are also obtained
assuming the Lorentz violation in each of the spacetime directions. We also
show some graphs that exhibit how the loop correction and the Lorentz violation
affect the the Casimir energy density and the mass of the scalar field.
