Fermionic Casimir interaction in cylinder-plate and cylinder-cylinder geometries

TL;DR

This paper investigates the Casimir effect for massless fermionic fields in cylinder-plate and cylinder-cylinder geometries, deriving explicit interaction formulas and analyzing asymptotic behaviors to support derivative expansion methods.

Contribution

It provides explicit formulas for fermionic Casimir interactions in complex geometries and compares asymptotic expansions to validate derivative expansion approaches.

Findings

Leading order matches proximity force approximation

Next-to-leading order results support derivative expansion ansatz

Explicit formulas for various cylinder configurations

Abstract

In this work, we consider the Casimir effect due to massless fermionic fields in the presence of long cylinders. More precisely, we consider the interaction between a cylinder parallel to a plate, between two parallel cylinders outside each other, and between a cylinder lying parallelly inside another cylinder. We derive the explicit formulas for the Casimir interaction energies and compute the leading and the next-to-leading order terms of the small separation asymptotic expansions. As expected, the leading order terms coincide with the proximity force approximations. We compare the results of the next-to-leading order terms of different quantum fields, and show that our results support the ansatz of derivative expansions.