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arXiv · 2503.13196

Scale-Dependent Suppression Functions and Functional Space Geometry in Renormalization

Daniel Ketels
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Abstract

We analyze the effects of a scale-dependent suppression function $\Omega(k, \Lambda)$ on the functional space geometry in renormalization theory. By introducing a dynamical cutoff scale $\Lambda$, the suppression function smoothly regulates high-momentum contributions without requiring a hard cutoff. We show that $\Omega(k, \Lambda)$ 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 $\Omega(k, \Lambda)$ 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.

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Daniel Ketels. 2025-03-17. Scale-Dependent Suppression Functions and Functional Space Geometry in Renormalization. https://arxiv.org/abs/2503.13196

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