arXiv subjects

Daniel Ketels

Publications and source records attributed to Daniel Ketels.

3 recordsLinked to original sources

arXiv2025

Scale-Dependent Suppression Functions and Functional Space Geometry in Renormalization

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.

math-ph↗

arXiv2025

Intrinsic Regularization via Curved Momentum Space: A Geometric Solution to Divergences in Quantum Field Theory

The problem of UV divergences in QFT has long been a fundamental challenge. Standard regularization techniques modify high-energy behavior to ensure well-defined integrals. However, these approaches often introduce unphysical parameters, rely on arbitrary prescriptions, or break fundamental symmetries, making them mathematically effective but conceptually unsatisfactory. We propose a novel and self-consistent approach in which UV regularization emerges naturally from the curved geometry of momentum space. Through curved momentum space, imposed by a geodesic metric, we construct an integral measure that inherently suppresses high-energy divergences while preserving fundamental symmetries, including full Lorentz invariance. This framework is self-sufficient, i.e. requires no external regulators. It retains equations of motion and is fully compatibility with standard field theory Our approach guarantees the weakest possible suppression necessary for convergence, avoiding excessive modifications to quantum behavior, still achieving convergence. While formulated in Riemannian Geometry, we show seamless extension to Minkowski space, maintainining regularization properties in relativistic QFT. This offers an alternative to ad hoc renormalization, providing an intrinsic and mathematically well-motivated suppression mechanism, purely rooted in curved geometry of momentum space. We rigorously construct the measure-theoretic framework and demonstrate its effectiveness by proof of finiteness for key QFT integrals. Beyond resolving divergences, this work suggests broader applications in spectral geometry, effective field theory, and potential extensions to quantum gravity.

hep-th↗

arXiv2024

Efficient Approximation of Centrality Measures in Uncertain Graphs

In this thesis I propose an algorithm to heuristically calculate different distance measures on uncertain graphs (i.e. graphs where edges only exist with a certain probability) and apply this to the heuristic calculation of harmonic closeness centrality. This approach is mainly based on previous work on the calculation of distance measures by Potamias et al. and on a heuristic algorithm for betweenness centrality by Chenxu Wang and Ziyuan Lin. I extend on their research by using the concept of possible shortest paths, applying them to the afformentioned distances. To the best of my knowledge, this algorithmic approach has never been studied before. I will compare my heuristic results for harmonic closeness against the Monte Carlo method both in runtime and accuracy. Similarly, I will conduct new experiments on the betweenness centrality heuristic proposed y Chenxu Wang and Ziyuan Lin to test its efficacy on a bigger variety of instances. Finally, I will test both of these algorithms on large scale graphs to evaluate the scalability of their runtime.

cs.DM↗