Non-perturbative quantum dynamics on embedded submanifolds: from geometric mass to Higgs potentials

We establish a quantum dynamics framework for curved submanifolds embedded in higher-dimensional spaces. Through rigorous dimensional reduction, we derive the first complete Schrödinger 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. We hypothesize that geometric induction can produce Higgs-mechanism-type potentials. Under this working hypothesis, particle masses arise solely from submanifold embedding geometry and matter–field couplings are encoded in curvature invariants. If this hypothesis holds, it would enable experimental access to higher-dimensional physics at all energy scales through geometric induction. We also discuss the Higgs vacuum near small-mass black holes.