🔢 Category

math-ph

3366 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.

🔢 mathematics

Multitrace Müller Boundary Integral Equation for Electromagnetic Scattering by Composite Objects

This paper presents a well-conditioned, second-kind boundary integral equation for time-harmonic electromagnetic scattering by composite dielectric objects, achieved by extending the classical Müller formulation via the global multitrace method and Stratton-Chu representation, and solved efficiently using a Petrov-Galerkin discretization with Rao-Wilton-Glisson and Buffa-Christiansen functions.

Van Chien Le, Kristof Cools2026-06-12
⚛️ high-energy theory

Analytic approaches to perturbations of strongly coupled Yang-Mills plasma

This paper analyzes perturbations of strongly coupled Yang-Mills plasma by demonstrating that while classical spectral truncation methods are limited by convergence boundaries, an exact WKB analysis combined with Seiberg--Witten theory provides a systematic framework to resum quasinormal modes, yielding an accurate spectrum that remains valid from the large wave number regime all the way to zero.

Inês Aniceto, Paolo Arnaudo, Alex Ratcliffe, Michał Spaliński2026-06-12
🔢 mathematics

The μ\mu-extension of iterated integrals and nested sums

This paper constructs μ\mu-extensions for iterated integrals and associated nested sums arising in perturbative quantum field theory calculations, demonstrating that while these extensions generally preserve the underlying Hopf algebra structure and map into the same function space polynomially in μ\mu, they lead to higher transcendental functions specifically in cases involving square-root valued alphabets or central binomials.

J. Blümlein, A. M. Gavrilik, U. Y. Lunga, O. Mykhailiv2026-06-12
🔢 mathematics

The censored stochastic six-vertex model and parabolic Kazhdan--Lusztig RR-polynomials

This paper introduces a censored stochastic six-vertex model, demonstrating that its blocking measure stochastically dominates the system at all times to control second-class particles, a result established through connections to Iwahori--Hecke algebras and the use of parabolic Kazhdan--Lusztig RR-polynomials as both explanatory tools and intertwining kernels.

Hindy Drillick, Levi Haunschmid-Sibitz2026-06-12
🔢 mathematics

Chiral Long-Range Order in three Euclidean Lattice Gross-Neveu Models

This paper rigorously proves the existence of long-range order in the chirally charged fermion-mass bilinear for a class of two-dimensional Euclidean lattice Gross-Neveu models with even flavor numbers by utilizing reflection positivity, chessboard estimates, and Peierls-type arguments to establish a non-perturbative connection between the lattice theory and large-NN mean-field predictions across various discretizations.

Simone Fabbri, Leonardo Goller2026-06-12
🔢 mathematics

Kubo-Martin-Schwinger conditions for non-Hermitian systems

This paper establishes that for diagonalizable non-Hermitian Hamiltonians with real spectra, the biorthogonal Gibbs functional satisfies the Kubo-Martin-Schwinger (KMS) condition if and only if the system is quasi-Hermitian, thereby providing a metric-free characterization of quasi-Hermiticity and proving that the resulting KMS states cannot be simply deduced from their Hermitian counterparts via similarity transformations.

Chen Lan, Luyao Ma, Hao Yang2026-06-12
🔢 mathematics

Rapid mixing for Gibbs measures in Riemannian manifolds

This paper establishes conditions involving manifold curvature, inverse temperature, and escaping directions from saddle points that guarantee polynomial mixing times for Langevin dynamics to Gibbs measures on Riemannian manifolds, thereby avoiding barren plateaus and spurious local minima through a novel relation between processes in the domain and their Riemannian submersion images.

Ángela Capel, Marco Castrillón-López, Sofyan Iblisdir, Angelo Lucia, Pablo Páez-Velasco, David Pérez-García2026-06-12