Non-perturbative Quantum Dynamics on Embedded Submanifolds: From Geometric Mass to Higgs Potentials

• URL: http://arxiv.org/abs/2506.07337v4
• Date: Sat, 05 Jul 2025 19:01:27 GMT
• Title: Non-perturbative Quantum Dynamics on Embedded Submanifolds: From Geometric Mass to Higgs Potentials
• Authors: Li Wang, Run Cheng, Jun Wang,
• Abstract summary: We establish a quantum dynamics framework for curved submanifolds embedded in higher-dimensional spaces.<n>We derive the first complete Schr"odinger and Klein-Gordon equations incorporating non-perturbative geometric interactions-resolving ambiguities in constrained quantization.<n>We also discuss the Higgs vacuum near small-mass black holes.
• Score: 8.008496553380805
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We establish a quantum dynamics framework for curved submanifolds embedded in higher-dimensional spaces. Through rigorous dimensional reduction, we derive the first complete Schr\"{o}dinger and Klein-Gordon equations incorporating non-perturbative geometric interactions-resolving ambiguities in constrained quantization. Crucially, extrinsic curvature of the ambient manifold governs emergent low-dimensional quantum phenomena. Remarkably, this mechanism generates scalar field masses matching Kaluza-Klein spectra while eliminating periodic compactification requirements. Geometric induction concurrently produces Higgs mechanism potentials. Particle masses emerge solely from submanifold embedding geometry, with matter-field couplings encoded in curvature invariants. This enables experimental access to higher-dimensional physics at all energy scales through geometric induction. We also discuss the Higgs vacuum near small-mass black holes.

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