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arXiv · 2609.08378

Scalar Casimir Effect on a Two-Dimensional Sphere with a Wu--Yang Magnetic Monopole

Jun-Cheng Zhang·Xiao-Yin Pan·Juhao Wu·Qing-hai Wang
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Abstract

We investigate the Casimir effect of a complex scalar field on a two-dimensional sphere threaded by a fixed Wu--Yang magnetic monopole at the center. In this background the charged scalar field is a section of a nontrivial complex line bundle over $S^2$, reflecting the monopole's nontrivial topology. We solve the Klein--Gordon equation analytically and compute the Casimir energy using a generalized Abel--Plana formula for multivalued functions. We find that the monopole can reverse the sign of the Casimir pressure, turning an attractive force into a repulsive one when the monopole strength is sufficiently large. This behavior persists across a broad range of curvature couplings and suggests that Wu--Yang monopoles may provide a source of repulsive vacuum stress, with possible implications for gravitational and cosmological settings.

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Jun-Cheng Zhang, Xiao-Yin Pan, Juhao Wu, Qing-hai Wang. 2026-09-08. Scalar Casimir Effect on a Two-Dimensional Sphere with a Wu--Yang Magnetic Monopole. https://arxiv.org/abs/2609.08378

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