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Parity-dependent Casimir forces and Hall currents for a confined Dirac field

Aitor Fernández and César D. Fosco

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Phys. Rev. D 113, 125007 – Published 4 June, 2026

DOI: https://doi.org/10.1103/22t8-k1q8

Abstract

We study a massless Dirac field subjected to two alternative boundary conditions on two parallel thin walls, in d+1 dimensions. The two configurations correspond to the system being even or odd under reflection about the midplane between the two walls, and lead to qualitatively different behaviors. The even (symmetric) configuration produces an attractive Casimir force, whereas the odd (antisymmetric) one yields repulsion, in agreement with a general theorem linking parity to the sign of the fermionic Casimir effect. We complement this result by studying two phenomena associated with the vacuum fluctuations responsible for the Casimir interaction, both of which are also sensitive to parity: the correlation between currents concentrated on the walls, and the induced bulk current under the influence of an external electric field. For the latter we show that, in 2+1 dimensions, an induced transverse (Hall-like) current arises, whose spatial profile inherits the symmetry of the confining potential.

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Phys. Rev. D 113, 125007– Published 4 June, 2026
  • Received 10 March 2026
  • Accepted 15 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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