Lattice Fermionic Casimir effect in a Slab Bag and Universality

TL;DR

This paper investigates the lattice fermionic Casimir effect using MIT Bag boundary conditions, demonstrating universality and resolving previous oscillation issues in naive fermion calculations through extrapolation techniques.

Contribution

It applies MIT Bag boundary conditions to lattice fermions and shows that naive fermion results align with continuum expressions after extrapolation, confirming universality.

Findings

Naive, Wilson, and overlap fermions match continuum results at zero lattice spacing.

Oscillations in naive fermion Casimir energy are eliminated with extrapolation.

Naive fermion results are consistent with other fermion types after correction.

Abstract

We apply the physically more appealing MIT Bag boundary conditions to study the Casimir effect on the lattice. Employing the formalism of arXiv:2005.10758 to calculate the Casimir energy for free lattice fermions, we show that the results for the naive, Wilson and overlap fermions match the continuum expressions precisely in the zero lattice spacing limit, as expected from universality. In contrast to arXiv:2005.10758 where the result for the naive fermions rapidly oscillates with the lattice size for both, the periodic (P) and anti-periodic (AP) boundary conditions, no oscillations are observed with the lattice size. Furthermore, the apparent violation of the universality for naive fermion in arXiv:2005.10758 is shown to be cured by applying suitable series extrapolation techniques, thus demonstrating that the Casimir energy for the naive fermions with periodic/antiperiodic boundary conditions agrees with the results for other free lattice fermions, and can as well be used to obtain the results for the Dirac fermion in the zero limit of the lattice spacing.