Non-perturbative Quantum Dynamics on Embedded Submanifolds: From Geometric Mass to Higgs Potentials
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911301000757248 |
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| author | Wang, Li Cheng, Run Wang, Jun |
| author_facet | Wang, Li Cheng, Run Wang, Jun |
| contents | 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. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_07337 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-perturbative Quantum Dynamics on Embedded Submanifolds: From Geometric Mass to Higgs Potentials Wang, Li Cheng, Run Wang, Jun General Relativity and Quantum Cosmology Mathematical Physics Quantum Physics 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. 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. |
| title | Non-perturbative Quantum Dynamics on Embedded Submanifolds: From Geometric Mass to Higgs Potentials |
| topic | General Relativity and Quantum Cosmology Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2506.07337 |