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arXiv:2607.15070

Casimir effect for a massive scalar field confined between parallel plates with a spatially varying effective mass

R. L. Araújo Xavier, M. H. B. Chaves, E. R. Bezerra de Mello, Herondy Mota

hep-thgr-qcmath-phquant-phSubmitted Jul 16, 2026• Announced Jul 17, 2026• Revised Sep 25, 2026 (v2)

v1 · Jul 16, 2026 v2 · Sep 25, 2026

Abstract

We investigate the Casimir effect for a massive real scalar field confined between two perfectly reflecting parallel plates in the presence of a position-dependent effective mass, a mechanism for coupling a scalar background to a scalar field. Exact normal modes are obtained by solving the corresponding Klein-Gordon equation, leading to a transverse energy spectrum that exhibits a characteristic Landau-like structure despite the absence of an external magnetic field. Upon quantization of the field, the vacuum energy is evaluated by means of generalized zeta-function regularization together with an appropriate renormalization procedure. The renormalized vacuum energy naturally separates into a Landau-like contribution and an additional term induced by the spatial dependence of the effective mass. We show analytically and numerically that both contributions are exponentially suppressed in the strong-coupling regime. In the opposite limit, the Landau-like contribution smoothly reproduces the standard vacuum energy for a massive scalar field confined between parallel plates, whereas the additional contribution becomes singular owing to the restricted domain of validity of the exact spectrum. Except in the vicinity of this singular limit, the vacuum energy is shown to be dominated by the Landau-like sector. Our results establish a direct connection between position-dependent effective masses and boundary-induced quantum vacuum phenomena, providing a new exactly solvable framework for the investigation of Casimir effects in spatially inhomogeneous relativistic systems.

Comments: 13 pages, 3 figures, accepted for publication in Physics Letters B

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. In this scenario, we calculate the vacuum energy density and its first-order correction in the coupling constants of the theory. Additionally, we consider the mass correction for each field separately, namely the topological mass that arises from the boundary conditions imposed on the fields and which also depends on the coupling constants. To develop this analysis, we use the mathematical formalism known as the effective potential, expressed as a path integral in quantum field theory.

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