Effect of boundary conditions on dimensionally reduced field-theoretical models at finite temperature

Here we understand dimensional reduction as a procedure to obtain an effective model in D−1 dimensions that is related to the original model in D dimensions. To explore this concept, we use both a self-interacting fermionic model and self-interacting bosonic model. Furthermore, in both cases, we consider different boundary conditions in space: periodic, antiperiodic, Dirichlet, and Neumann. For bosonic fields, we get the so-defined dimensional reduction. Taking the simple example of a quartic interaction, we obtain that the boundary conditions (periodic, Dirichlet, Neumann) influence the new coupling of the reduced model. For fermionic fields, we get the curious result that the model obtained reducing from D dimensions to D−1 dimensions is distinguishable from taking into account a fermionic field originally in D−1 dimensions. Moreover, when one considers antiperiodic boundary conditions in space (both for bosons and fermions), it is found that the dimensional reduction is not allowed.