Casimir effect on the lattice spacetime

Fujii, Daisuke; Nakayama, Katsumasa*; Suzuki, Kei   

We investigate the characteristics of Casimir energy within a lattice-regularized spacetime framework. Typically, Casimir energy requires a regularization procedure to remove divergences originating from vacuum fluctuations of quantum fields. In this work, we adopt lattice regularization, wherein discretization effects persist as long as the lattice spacing remains finite. We first detail how the Casimir energy is computed using both naive and Wilson fermion formulations. When discretization artifacts are limited to only a few lattice points, it becomes possible to recover the continuum Casimir energy by taking the continuum limit. To illustrate physical applications, we evaluate the Casimir energy for electron fields in Dirac/Weyl semimetals, where lattice effects are meaningfully retained, and for photon fields in axion electrodynamics, where the continuum limit is accurately reproduced.