A note on "Algebraic approach to Casimir force between two $\delta$-like potentials" (K. Ziemian, Ann. Henri Poincar\'e, Online First, 2021)

TL;DR

This paper clarifies the relationship between recent and prior work on Casimir energy densities involving delta-like potentials, confirming their equivalence despite different methods used.

Contribution

It demonstrates that the Casimir energy density for a single delta-like potential is consistent across different approaches, correcting previous claims.

Findings

Casimir energy density for delta-like potentials is consistent across methods

The recent work's results agree with earlier findings

Clarifies the relation between different theoretical approaches

Abstract

We comment on the recent work [1], and on its relations with our papers [2,3] cited therein. In particular we show that, contrarily to what stated in [1], the Casimir energy density determined therein in the case of a single delta-like singularity coincides with the energy density obtained previously in our paper [2] using a different approach.