📝 SummarXiv

Abstract

Quantum gravity corrections to the behavior of matter, such as Higgs bosons and fermions, are notoriously difficult to calculate. The standard tools of quantum field theory often break down, producing infinite results that spoil our predictions. This work introduces a new geometric method, called Topological Regularization (TR), to solve this problem. The key idea is to temporarily "wrap" flat spacetime into a compact, curved shape (specifically, a four-dimensional sphere). This curvature naturally introduces a high-energy cutoff that prevents infinities without violating fundamental symmetries like Lorentz invariance. We apply this method to calculate one- and two-loop quantum gravity corrections to processes involving fermions and the Higgs boson. The results are not only finite but are directly governed by a single number describing the shape of the spacetime: its Euler characteristic. This reveals a profound link between the ultraviolet (UV) behavior of high energies and the infrared (IR) interactions of low energies. Furthermore, the mathematical form of our regulator suggests a thermal interpretation, drawing a fascinating connection to the heat felt by an accelerating observer (the Unruh effect). While the predicted effects are incredibly small and currently beyond experimental reach, this framework provides a symmetry-preserving, geometric path to exploring physics at the Planck scale.