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

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.