1695 papers
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.
This paper establishes a generalized Peierls-Onsager substitution for periodic elliptic pseudo-differential operators under a local spectral gap, utilizing strongly localized tight-frames and magnetic matrices to extend validity to long-range magnetic fields without slow-variation or triviality assumptions while providing precise error control for approximate time evolution.
This paper generalizes the AKSZ construction to multisymplectic sigma models by equipping the target -manifold with an arbitrary-degree closed form, thereby providing a unified, higher-derivative gauge-invariant framework that reformulates diverse theories such as higher-dimensional Chern-Simons theory, MacDowell-Mansouri-Stelle-West action, and self-dual gravity while connecting to standard multisymplectic formulations in PDE geometry.
This paper presents an ultrafast electrostatic modeling framework for plasmonic nanoparticles of arbitrary geometry that achieves rapid spectral response calculations by projecting the Neumann-Poincaré operator onto a compact dipole basis to avoid large eigenproblems, while incorporating retardation effects via the modified long-wavelength approximation.
This paper presents a stochastic analysis of fifth-order KdV soliton momentum in a damping regime, deriving explicit amplitude-dependent representations within a Gaussian random framework and demonstrating that the nonlinear momentum evolution equation reduces to the Painlevé II equation under dominant approximation.
This paper develops a homotopy categorification of Hopf algebras called Hopf 2-algebras to construct 2-quantum doubles and 2--matrices, demonstrating that their representation 2-categories form braided monoidal structures and admit Lie 2-bialgebras as a semiclassical limit.
This paper develops a general theory of 3-dimensional orbifold completion by constructing a Morita category of -algebras within a Gray category with duals to describe generalized orbifolds and their defects in topological quantum field theories, thereby enabling the construction of universal state sum models and unifying recent results on Witt equivalent Reshetikhin–Turaev theories.
This paper classifies all Nijenhuis operators on 2-dimensional complex pre-Lie algebras and 3-dimensional complex associative algebras, utilizing these operators to derive solutions to the classical Yang-Baxter equation on their corresponding sub-adjacent Lie algebras.
This paper introduces a direct and explicit construction of a scalar pseudodifferential asymmetry operator of order $-3$ for the curl operator on a closed oriented Riemannian 3-manifold, which generalizes the classical eta invariant and encodes spectral asymmetry information through microlocal analysis.
This paper demonstrates that the Zernike system is equivalent to the Higgs oscillator on a sphere or pseudosphere, showing that its non-Hermitian nature is merely an artifact of an imaginary gauge that can be removed via a canonical transformation to reveal a Hermitian free particle system under specific parameter conditions.
This paper extends Kramers' law to bistable systems driven by fast chaotic dynamics rather than unbounded noise, demonstrating through a reduced-order AMOC model that this "chaotic Kramers' law" accurately predicts transition times and offers insights into recent AMOC collapses and recoveries observed in complex climate models.