arXiv subjects

Sebastián Alí Sacasa-Céspedes

Publications and source records attributed to Sebastián Alí Sacasa-Céspedes.

4 recordsLinked to original sources

arXiv2026

Topological Regularization

This work introduces topological regularization as a framework for handling ultraviolet divergences in quantum field theory, reinterpreting infinities as topological obstructions at spacetime boundaries. Through geometric compactification via stereographic projection, singularities are reframed as boundary artifacts. The framework employs causal embeddings and the causality group to preserve Lorentz invariance and unitarity, while homotopy-equivalent defect structures guarantee regularization independence via Stokes-Poincaré duality. The Physical Equivalence Theorem shows that homotopy-equivalent schemes yield identical renormalized observables. Renormalization group flows are governed by Euler characteristics, and anomalies are resolved through cobordism and Chern character integrals. This approach unifies UV/IR duality, anomaly cancellation, and Osterwalder-Schrader reconstruction. Applications extend to AdS/CFT, PDEs, quantum simulators, and noncommutative geometry. Topological regularization replaces artificial cutoffs with intrinsic geometric mechanisms, positioning spacetime as a defect-entangled structure governed by topological invariants, with testable predictions in quantum materials.

physics.gen-ph↗

arXiv2026

First-Principles Prediction of Material Properties from Topological Invariants

Methods for predicting material properties often rely on empirical models or approximations that overlook the fundamental topological nature of quantum interactions. We introduce a topological framework based on string theory and graph geometry that resolves ultraviolet divergences as topological obstructions regularized via Calabi-Yau mappings while preserving symmetries and causal structures, where molecular and condensed matter systems are represented combinatorially through a graph where M-branes form vertices and open strings are twistor-valued edges, holomorphically encoding geometric data from the dynamical system. The resulting effective action is governed by a graph Laplacian whose spectrum dictates stability, excitations, and phase transitions. Applied to uniaxial nematic liquid crystals, the model not only recovers the phenomenological virtual volumes of the Jiron-Castellon model from first principles but also predicts anisotropic thermal expansion coefficients and refractive indices with precision exceeding 0.06\%. The quantitative agreement with experiment, achieved without fitted parameters, demonstrates that principles from quantum gravity and string theory can directly yield accurate predictions for complex materials.

physics.gen-ph↗

arXiv2026

On Geometric Evolution and Microlocal Regularity of the Navier-Stokes Equations

We propose a microlocal-Riemannian framework for the three-dimensional incompressible Navier-Stokes equations on a smooth oriented Riemannian manifold (M,g). The dynamics is lifted to the unit cosphere bundle S*M via a normal-coordinate microlocal transform whose construction is justified by the positive homogeneity of the principal symbol of the linearised system in the cotangent fiber variable. Once the velocity field is fixed, the lifted dynamics is a linear non-autonomous transport-dissipation equation on a compact phase space; its coefficients encode intrinsic geometric quantities of the original flow. We introduce a microlocal energy, an angular volume functional and a directional entropy, and analyse their dissipation along the lifted dynamics. An effective affine connection encodes the back-reaction of the velocity gradient on the geometry of S*M and gives rise to a Ricci-type microlocal evolution. The framework yields a sharp geometric equivalence: a smooth solution fails to extend past time T if and only if at least one of three intrinsic microlocal controls -- deformation integrability, directional-entropy boundedness, or lifted-energy boundedness -- fails. A dimensional analysis exhibits a symmetry-lock phenomenon, in which the asymptotic vanishing of the volume of fibers enforces angular isotropy and topologically obstructs the formation of microlocal angular singularities. The framework is illustrated explicitly on the flat torus, where every assumption is verified, and is extended to the Euclidean setting under a uniform-coordinate hypothesis. The global regularity problem is not resolved here; rather, it is recast as a structural-stability question for a compact, symmetry-constrained, microlocally coercive evolution system, with the role of viscosity made explicit through spectral coercivity.

physics.gen-ph↗

arXiv2025

Topological Regularization of 1 Loop and 2 Loop Gravitational Corrections in the Higgs Fermion Sector

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.

physics.gen-ph↗