Casimir Effect for Nonlocal Field Theories with Continuum Massive Modes

In this paper, we study the Casimir force for a class of Lorentzian nonlocal field theories. These theories include a continuum of massive excitations. In this regard, the effect of continuum massive modes on Casimir force is of interest. We focus on the simplest case of two absorbing parallel planes in 1+1 dimensions, and we show that unlike local field theories, the thickness of the absorbing “walls” changes the value of Casimir force.