Geometry-Induced Vacuum Polarization and Mode Shifts in Maxwell-Klein-Gordon Theory

Abstract

Geometric confinement is known to modify single-particle dynamics through effective potentials, yet its imprint on the interacting quantum vacuum remains largely unexplored. In this work, we investigate the Maxwell--Klein--Gordon system constrained to curved surfaces and demonstrate that the geometric potential ${\Sigma }_{\mathrm{geom}}(\mathbf{r})$ acts as a local renormalization environment. We show that extrinsic curvature modifies the scalar loop spectrum, entering the vacuum polarization as a position-dependent mass correction $M^2(\mathbf{r})\to m^2+{\Sigma }_{\mathrm{geom}}(\mathbf{r})$. This induces a finite, gauge-invariant ``geometry-induced running'' of the electromagnetic response. In the long-wavelength regime ($|\mathbf{Q}|R\ll 1$), we derive a closed-form expression for the relative frequency shift $\Delta \omega /\omega$, governed by the overlap between the electric energy density and the geometric potential. Applying this formalism to Gaussian bumps, cylindrical shells, and tori, we identify distinct spectral signatures that distinguish these quantum loop corrections from classical geometric optics. Our results suggest that spatial curvature can serve as a tunable knob for ``vacuum engineering,'' offering measurable shifts in high-$Q$ cavities and plasmonic systems.

References in corpus (13)

• Chiral tunneling and the Klein paradox in graphene
• Topological Photonics
• Quantum fluids of light
• Graphene Plasmonics: Challenges and Opportunities
• Fiber-optical analogue of the event horizon
• Measurement of stimulated Hawking emission in an analogue system
• Casimir forces between arbitrary compact objects
• Effective Action of Vacuum: Semiclassical Approach
• Quantum mechanics on curved 2D systems with electric and magnetic fields
• Renormalization, running couplings and decoupling for the Yukawa model in curved spacetime
• Quantum search in many-body interacting system with long-range interaction
• Resummed heat-kernel for surface contributions: Dirichlet semitransparent boundary conditions
• Non-perturbative Quantum Dynamics on Embedded Submanifolds: From Geometric Mass to Higgs Potentials