Casimir Effect for Massless Fermions in One Dimension: A Force Operator Approach

TL;DR

This paper investigates the Casimir force between two scatterers in a one-dimensional massless Dirac fermion background, revealing tunable attractive or repulsive interactions based on spinor polarization.

Contribution

It introduces a force operator approach to calculate the Casimir effect for massless fermions, including the effects of scatterer properties and polarization.

Findings

Identifies conditions for attractive, repulsive, or null Casimir forces.

Derives the force for finite width barriers and their zero-width limit.

Shows the force depends on the relative spinor polarizations of scatterers.

Abstract

We calculate the Casimir interaction between two short range scatterers embedded in a background of one dimensional massless Dirac fermions using a force operator approach. We obtain the force between two finite width square barriers, and take the limit of zero width and infinite potential strength to study the Casimir force mediated by the fermions. For the case of identical scatterers we recover the conventional attractive one dimensional Casimir force. For the general problem with inequivalent scatterers we find that the magnitude and sign of this force depend on the relative spinor polarizations of the two scattering potentials which can be tuned to give an attractive, a repulsive, or a compensated null Casimir interaction.