https://doi.org/10.1140/epjp/s13360-025-07144-9
Regular Article
Scalar field with a semi-transparent Neumann mirror and sources
1
Unaffiliated, Itajubá, MG, Brazil
2
IFQ, Universidade Federal de Itajubá, Av. BPS 1303, Pinheirinho, Caixa Postal 50, 37500-903, Itajubá, MG, Brazil
3
Unaffiliated, Niterói, RJ, Brazil
4
Departamento de Física, Universidade Federal de Lavras, Caixa Postal 3037, 37200-900, Lavras, MG, Brazil
a
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Received:
29
September
2025
Accepted:
1
December
2025
Published online:
13
December
2025
Abstract
In this paper, we explored the Klein–Gordon field theory in (
) dimensions in the presence of a (
)-dimensional hyperplanar 
-like potential that couples quadratically to the field derivatives. This model effectively generalizes the Neumann boundary condition for the scalar field on the plane, as it becomes equivalent to this condition in an appropriate limit of the coupling parameter. Specifically, we calculated the modifications to the Feynman propagator induced by the planar potential and analyzed the interaction energy between a stationary point-like source and the potential, obtaining a general and exact expression. We demonstrated that, under certain conditions relating the field mass and the coupling constant to the external potential, the vacuum state becomes unstable, giving rise to a pair creation phenomenon that resembles the Schwinger effect in quantum electrodynamics.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
