  In this study, we consider the four-dimensional Maxwell electrodynamics
extended with CPT-even Myers-Pospelov Lorentz-violating dimension-six operators
to investigate the associated two-dimensional properties in the context of
quantum vacuum fluctuation effects, namely, the Casimir effect. Upon projecting
out the 4D theory down to a 2D theory we obtain analogs of these operators
leading to a modified dispersion relation in a Lorentz invariance violation
(LIV) scalar model equivalent to the electromagnetic theory. By making use of
the modified dispersion relation, we derive exact analytic expressions for the
Casimir energy and force induced by imposing Dirichlet boundary conditions on
the scalar field. In the regime where the LIV parameter becomes very small, we
recover known results for the Casimir energy and force plus correction terms
due to the LIV.
