3190 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 investigates surface defects in four-dimensional and class theories on lens spaces by deriving closed-form difference operators that generate a Sklyanin algebra and proposing that these operators correspond to transfer matrices of inhomogeneous spin chains.
This paper employs neural networks within a crossing-symmetric dispersion relation bootstrap framework to simultaneously learn the mass spectrum and partial-wave coefficients of tree-level open superstrings, deriving bounds on Wilson coefficients and identifying the Virasoro-Shapiro amplitude while analyzing transitions in non-dual amplitudes.
This paper establishes the exact spectral integrability of a finite-channel random Schrödinger operator in the unitary symmetry class by mapping its Riccati dynamics to a free-fermion gas, which yields a multichannel generalization of Halperin–Thouless formulas via a Kontsevich-type matrix Airy integral and reveals a universal spectral edge profile governed by the tritronquée solution of Painlevé I.
This paper proves the concentration conjecture for three-dimensional Dirac-Coulomb operators by demonstrating that the lowest eigenvalue in the spectral gap is minimized when all charge is concentrated at a single point, utilizing a strict two-center estimate and Birman-Schwinger comparison to establish this lower bound for both point charges and general nonnegative finite charge measures.
This paper identifies that standard spatial filtering on the sphere fails to commute with differential operators due to intrinsic curvature, and proposes a unique generalized spherical convolution that ensures consistency with physics by commuting with radial projection, divergence, and curl, thereby eliminating spurious errors in coarse-grained dynamics.
This paper develops a twisted Marchenko lemma to derive nonlinear equations for two-component Wronski matrices, yielding non-commutative two-component KP, Burgers, DS, and NLS equations through direct quasi-Wronskian approaches and various reductions.
This paper investigates the quasiparticle dispersion relation of a weakly coupled homogeneous Bose gas beyond the Bogoliubov approximation, demonstrating that first-order corrections in both canonical and grand-canonical settings preserve a linear phonon behavior at small momenta with a computable velocity.
This paper demonstrates that the Yamazaki-Hori solution to the Ernst equation can be expressed in Pfaffian form, a result that sheds new light on Nakamura's conjecture regarding the relationship between the Ernst equation and the 2D Toda model.
This paper extends the study of the ABC-equation by constructing new quasi-integrable structures and analyzing their actions on symmetries and cosymmetries, building upon the findings of its predecessor.
This paper presents a method using SIREN neural networks to create continuous, differentiable, and grid-free representations of the sea surface from time-sequenced lidar point clouds, demonstrating their ability to accurately reconstruct wave fields, filter noise, and enable directional wave analysis with errors comparable to instrument precision.