Vacuum energy density from a self-interacting scalar field in a Lorentz-violation Hořava-Lifshitz model

In this paper we consider a massive self-interacting scalar quantum field in a Lorentz-violation scenario based on a Hořava-Lifshitz model. Specifically, we investigate the vacuum energy density and its loop correction, up to first order in the self-interaction coupling constant, and also the topological mass generation. These quantities are also analyzed in the case where the field is massless. The scalar vacuum state is perturbed by the presence of two large parallel plates, placed at a distance <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>L</a:mi></a:mrow></a:math> from each other, due to the imposition of the Dirichlet boundary condition on the two plates. To perform this study, the effective potential approach in quantum field theory is applied.