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arXiv:2610.03843

Comment on ''Chiral electromagnetic surface waves on Chern-Simons interfaces'' Phys.Rev.D114(2026)L051903 and on arXiv:2606.12513 by N. Kaloper

Igor Bandos, Bohdan Zvorskyi

hep-thastro-ph.COhep-phphysics.opticsquant-phSubmitted Oct 2, 2026• Announced Oct 5, 2026
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Abstract

We demonstrate that Maxwell electrodynamics interacting with a planar Chern-Simons interface does not have plane wave solutions localized on the interface. We re-examine the derivation of such waves presented by N. Kaloper in [Phys.Rev.D114(2026)L051903] and show that at an intermediate step certain terms were missed in an equation therein. Taking these terms into account changes the final conclusion of [Phys.Rev.D114(2026)L051903]. We also show that the method used in [arXiv:2606.12513 [hep-th]] to reproduce the same result is not consistent.

Comments
4 pages

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We demonstrate that Maxwell electrodynamics interacting with a planar Chern-Simons interface does not have plane wave solutions localized on the interface. We re-examine the derivation of such waves presented by N. Kaloper in [Phys.Rev.D114(2026)L051903] and show that at an intermediate step certain terms were missed in an equation therein. Taking these terms into account changes the final conclusion of [Phys.Rev.D114(2026)L051903]. We also show that the method used in [arXiv:2606.12513 [hep-th]] to reproduce the same result is not consistent.
Recently, Zabolotskii [Phys. Rev. E 77, 036603 (2008)] presented the Lax pair for a version of the reduced Maxwell--Bloch equations. This version was derived under considering the unidirectional propagation of a two-component electromagnetic pulse through an anisotropic two-level medium. We demonstrate that his derivation contains essential omission, which led to the wrong version of the reduced Maxwell--Bloch equations. We also point out that the Lax pair for correct version of these equations had been known in the most general anisotropic case.
We show that Maxwell theory with a codimension-111 Chern-Simons interface supports chiral electromagnetic surface waves on the interface, even when the bulk theory on both sides is conventional vacuum electrodynamics in infinite space. Solving the exact boundary value problem we find that the Chern-Simons interaction acts with opposite sign on the two helicities oriented along the interface, giving rise to one normalizable mode localized on the interface. This mode is a gapless chiral surface photon with linear dispersion and a frequency-independent index of refraction set by the Chern-Simons coefficient. This mode exists despite the absence of ambient material response or geometric confinement.
A reexamination of the results of my earlier paper [Phys. Rev. E 50, 3116 (1994)] is supplied using entirely straightforward methods, i.e., without appealing to operator formalism. This reexamination confirms the consistency of the work in that paper by extracting a term proportional to time that Dembrinski et al. [Phys. Rev. E 53, 4243 (1996)] claim is not present. The arguments of Dembinski et al. are not refuted, but it is pointed out that they are based upon methods within which one readily encounters paradoxes such [p${\mathrm{^}}^{2}$,p^]\ensuremath{\ne}0 and [x^,p^]\ensuremath{\ne}i^. The present exposition avoids such methods. Unfortunately I am not prepared to address their numerical results. This will have to await further investigation. However, an example of numerical results of my own is presented in order to illustrate the richness of the dynamics of the model. \textcopyright{} 1996 The American Physical Society.