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arXiv · 2512.10463

Thermal Casimir effect in $\kappa$-Minkowski space-time

Suman Kumar Panja·Vishnu Rajagopal
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Abstract

We study the finite temperature Casimir effect for parallel plates in the $\kappa$-Minkowski space-time. Using the Matsubara formalism and imposing the Dirichlet boundary conditions on a massless $\kappa$-scalar field, we compute the $\kappa$-deformed corrections to thermal Casimir free energy, pressure, entropy, and internal energy. Our results demonstrate that space-time non-commutativity enhances the attractive nature of the thermal Casimir force while preserving thermodynamic consistency; the system satisfies the Nernst theorem and laws of thermodynamics remain intact in $\kappa$-deformed space-time. Our analysis yields an upper bound on the deformation parameter as $a\leq10^{-18}m$. Furthermore, our results indicate that non-commutative effects become experimentally observable in Casimir effect studies when the ratio of the non-commutative scale to plate separation satisfies $a/L\leq 10^{-12}$. We also obtain the expression for Stefan-Boltzmann's law in $\kappa$-Minkowski space-time.

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Suman Kumar Panja, Vishnu Rajagopal. 2025-12-11. Thermal Casimir effect in $\kappa$-Minkowski space-time. https://doi.org/10.1016/j.nuclphysb.2026.117335

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