🔢 Category

math-ph

2548 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.

⚛️ general relativity

A Covariant Distributional Approach for Junctions in Torsional Locally Rotationally Symmetric Class II Spacetimes

This paper presents a rigorous, coordinate-independent framework for studying junctions in torsional spacetimes by extending distribution theory to curved manifolds with torsion, thereby deriving general differentiability conditions and applying them to Einstein-Cartan-Sciama-Kibble gravity to overcome the limitations of the traditional coordinate-dependent Israel-Darmois formalism.

Ujjwal Agarwal, Sante Carloni2026-08-13
🔢 mathematics

Isospectral majorization and isoperimetric inequalities for coherent states on the Bloch sphere

This paper establishes an isospectral version of the Lieb-Solovej inequality for SU(2)SU(2) coherent states, demonstrating that rearranging a density operator's eigenvalues in decreasing order along the monomial basis maximizes convex functionals of its Husimi function and Wehrl entropy, while also proving that spherical caps maximize Ky Fan norms and Schatten sums of Toeplitz operators with indicator symbols, thereby yielding new isoperimetric inequalities without relying on the classical spherical isoperimetric inequality.

Luis Daniel Abreu2026-08-13
🌀 nonlinear sciences

qq-Analogue of the degree zero part of a rational Cherednik algebra and generalised Van Diejen's Hamiltonians

This paper introduces a subalgebra Hgln\mathbb{H}^{\mathfrak{gl}_n} within the double affine Hecke algebra of type GLnGL_n as a qq-analogue of the degree zero part of a rational Cherednik algebra, establishes its structural properties including a flat deformation and double centraliser property, and applies these results to derive new integrable generalisations of Van Diejen's Hamiltonians for systems with external Morse potentials and multiple particle types.

Misha Feigin, Martin Vrabec2026-08-12
🔢 mathematics

Higher Abelian Quantum Double Models

This paper establishes a rigorous C∗C^*-algebraic framework for higher abelian quantum double models on arbitrary finite-dimensional simplicial complexes, fully characterizing their frustration-free ground states via logical operator algebras and identifying conditions under which the model's core algebra forms a Cartan pair to facilitate the classification of equilibrium states.

Jorge Acuña Flores, Giuseppe De Nittis, Javier Lorca Espiro2026-08-12
⚛️ general relativity

Particle Creation in a Cosmological Background in Analogy to the Schwinger Effect

This paper rigorously derives particle production in a cosmological FLRW background by modeling a long gravitational pulse analogous to the Schwinger effect, utilizing Heun equation connecting formulas to demonstrate that the resulting particle spectrum exhibits a Planckian distribution with a temperature inversely proportional to the duration of the scale change.

Walter D. van Suijlekom, Michael F. Wondrak, Heino Falcke2026-08-12
⚛️ quantum physics

Global Non-Identifiability of Fubini-Study Geometry from Complete One-Period Endpoint Data

This paper establishes a global non-identifiability theorem demonstrating that complete one-period endpoint data of periodically driven quantum systems are insufficient to reconstruct the period-averaged Fubini-Study geometry because the data determine only the monodromy conjugation path while leaving the specific unitary lift, which governs the intra-period geometric evolution, fundamentally ambiguous.

Rashid Ahmad2026-08-12
🔢 mathematics

Limiting Law of Local Fields for the Mean Field Ghatak-Sherrington Model

This paper establishes a central limit theorem for the non-centered cavity field in the high-temperature regime of the mean field Ghatak-Sherrington model with spin values {0,±1,…,±S}\{0,\pm1,\ldots,\pm S\}, proving that the limiting law of the local field is a random finite mixture of Gaussian distributions with a quantitative error bound derived via the moment method.

Yunhui Chen, Keaton Fierro2026-08-12