Scale-Dependent Suppression Functions and Functional Space Geometry in Renormalization
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917959684849664 |
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| author | Ketels, Daniel |
| author_facet | Ketels, Daniel |
| contents | We analyze the effects of a scale-dependent suppression function $Ω(k, Λ)$ on the functional space geometry in renormalization theory. By introducing a dynamical cutoff scale $Λ$, the suppression function smoothly regulates high-momentum contributions without requiring a hard cutoff. We show that $Ω(k, Λ)$ induces a modified metric on functional space, leading to a non-trivial Ricci curvature that becomes increasingly negative in the ultraviolet (UV) limit. This effect dynamically suppresses high-energy states, yielding a controlled deformation of the functional domain. Furthermore, we derive the renormalization group (RG) flow of $Ω(k, Λ)$ and demonstrate its role in controlling the curvature flow of the functional space. The suppression function leads to spectral modifications that suggest an effective dimensional reduction at high energies, a feature relevant to functional space deformations and integral convergence in renormalization theory. Our findings provide a mathematical framework for studying regularization techniques and their role in the UV behavior of function spaces. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_13196 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scale-Dependent Suppression Functions and Functional Space Geometry in Renormalization Ketels, Daniel Mathematical Physics High Energy Physics - Theory Functional Analysis We analyze the effects of a scale-dependent suppression function $Ω(k, Λ)$ on the functional space geometry in renormalization theory. By introducing a dynamical cutoff scale $Λ$, the suppression function smoothly regulates high-momentum contributions without requiring a hard cutoff. We show that $Ω(k, Λ)$ induces a modified metric on functional space, leading to a non-trivial Ricci curvature that becomes increasingly negative in the ultraviolet (UV) limit. This effect dynamically suppresses high-energy states, yielding a controlled deformation of the functional domain. Furthermore, we derive the renormalization group (RG) flow of $Ω(k, Λ)$ and demonstrate its role in controlling the curvature flow of the functional space. The suppression function leads to spectral modifications that suggest an effective dimensional reduction at high energies, a feature relevant to functional space deformations and integral convergence in renormalization theory. Our findings provide a mathematical framework for studying regularization techniques and their role in the UV behavior of function spaces. |
| title | Scale-Dependent Suppression Functions and Functional Space Geometry in Renormalization |
| topic | Mathematical Physics High Energy Physics - Theory Functional Analysis |
| url | https://arxiv.org/abs/2503.13196 |