math-ph papers | Gist.Science

Mathematical physics sits at the fascinating intersection where abstract equations meet the fundamental laws of our universe. This field uses rigorous mathematical tools to model everything from the behavior of subatomic particles to the curvature of spacetime, turning complex theories into testable predictions. It is the language through which physicists describe reality, bridging the gap between pure mathematics and physical observation.

On Gist.Science, we process every new preprint published in this category on arXiv to make these dense studies accessible to everyone. Whether you are a specialist or a curious reader, you will find both plain-language overviews and detailed technical summaries for each paper. Below are the latest mathematical physics papers from arXiv, curated to help you explore the cutting edge of theoretical science.

🔢 mathematics

Chern-Simons deformations of the gauged O(3) Sigma model on compact surfaces

This paper establishes the existence of solutions to the gauged Chern-Simons-O(3)-Sigma model on compact Riemann surfaces using topological methods, demonstrating that solutions exist for small deformation parameters with multiple solutions when vortex and antivortex counts differ, while proving global existence for any parameter value when these counts are equal, alongside numerical investigations on the sphere.

Rene I. Garcia-Lara2026-02-23

🔢 mathematics

Nonlocal-to-local $L^p$ -convergence of convolution operators with singular, anisotropic kernels

This paper establishes and quantifies the strong $L^p$ -convergence of nonlocal convolution operators with singular, anisotropic kernels to local differential operators with natural boundary conditions, extending previous results to include stronger singularities and providing explicit convergence rates.

Helmut Abels, Christoph Hurm, Patrik Knopf2026-02-23

🔢 mathematics

On the Limit of the Tridiagonal Model for $β$ -Dyson Brownian Motion

This paper investigates the Householder tridiagonalization of a G $\beta$ E process governed by $\beta$ -Dyson Brownian motion, proving that the limit of its fixed-size upper-left minors yields a dynamical $\beta$ -stochastic Airy operator whose eigenvalues correspond to the asymptotic behavior of the largest eigenvalues of the original process.

Alan Edelman, Sungwoo Jeong, Ron Nissim2026-02-20

🔢 mathematics

Higher-Order Linear Differential Equations for Unitary Matrix Integrals: Applications and Generalisations

This paper establishes that specific unitary matrix integrals relevant to random permutation statistics and the Riemann zeta function satisfy both first-order matrix and higher-order scalar linear differential equations, offering an efficient computational alternative to nonlinear Painlevé characterizations while demonstrating that these results extend to natural $\beta$ -generalizations.

Peter J. Forrester, Fei Wei2026-02-20

🔢 mathematics

Rigorous derivation of damped-driven wave turbulence theory

This paper provides a rigorous mathematical justification for damped-driven wave turbulence theory by proving that the stochastic dynamics of the nonlinear Schrödinger equation converge to a deterministic kinetic equation under specific scaling limits, thereby establishing a formal framework for the turbulent energy cascade observed in empirical studies.

Ricardo Grande, Zaher Hani2026-02-19

🔢 mathematics

The Levi-Civita connection and Chern connections for cocycle deformations of Kähler manifolds

This paper demonstrates that unitary cocycle deformations of covariant $\ast$ -differential calculi preserve complex structures and Chern connections as twists of their original forms, while establishing that the Levi-Civita connection on deformed Kähler manifolds decomposes into the direct sum of twisted holomorphic and anti-holomorphic Chern connections.

Jyotishman Bhowmick, Bappa Ghosh2026-02-19

🔢 mathematics

Numerical Solution of the Bardeen-Cooper-Schrieffer Equation for Unconventional Superconductors

This paper investigates the analytical properties and presents an efficient Galerkin-based numerical solution using B-splines for the Bardeen-Cooper-Schrieffer equation describing unconventional superconductors with long-range power-law interactions on a $d$ -dimensional lattice, with specific results demonstrated for a nodal superconductor on a two-dimensional square lattice.

Andreas A. Buchheit, Torsten Keßler, Sergej Rjasanow2026-02-19

🔢 mathematics

Finite elements for the space approximation of a differential model for salts crystallization

This paper proposes and validates a finite-element space discretization combined with implicit-explicit time marching to simulate salt crystallization in stone artifacts, extending previous one-dimensional models to higher dimensions while conducting sensitivity analysis, stability considerations, and convergence testing.

Alessandra Aimi, Gabriella Bretti, Giulia Di Credico, Francesco Freddi, Chiara Guardasoni, Mario Pezzella2026-02-19

🔢 mathematics

FEKAN: Feature-Enriched Kolmogorov-Arnold Networks

This paper introduces Feature-Enriched Kolmogorov-Arnold Networks (FEKAN), a parameter-efficient extension that enhances the computational efficiency, convergence speed, and predictive accuracy of existing KAN architectures through feature enrichment while maintaining their interpretability.

Sidharth S. Menon, Ameya D. Jagtap2026-02-19

🔢 mathematics

A Lorentzian Equivariant Index Theorem

This paper establishes a Lorentzian equivariant index theorem for twisted Dirac operators on compact globally hyperbolic spacetimes with timelike boundaries, demonstrating that the equivariant index under APS boundary conditions follows the same fixed-point integral formula as in the Riemannian case through a novel reduction technique linking the equivariant index to spectral flow.

Onirban Islam, Lennart Ronge2026-02-19

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math-ph

Chern-Simons deformations of the gauged O(3) Sigma model on compact surfaces

Nonlocal-to-local LpL^pLp-convergence of convolution operators with singular, anisotropic kernels

On the Limit of the Tridiagonal Model for βββ-Dyson Brownian Motion

Higher-Order Linear Differential Equations for Unitary Matrix Integrals: Applications and Generalisations

Rigorous derivation of damped-driven wave turbulence theory

The Levi-Civita connection and Chern connections for cocycle deformations of Kähler manifolds

Numerical Solution of the Bardeen-Cooper-Schrieffer Equation for Unconventional Superconductors

Finite elements for the space approximation of a differential model for salts crystallization

FEKAN: Feature-Enriched Kolmogorov-Arnold Networks

A Lorentzian Equivariant Index Theorem

Nonlocal-to-local $L^p$ -convergence of convolution operators with singular, anisotropic kernels

On the Limit of the Tridiagonal Model for $β$ -Dyson Brownian Motion