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.

Conformally flat factorization homology in Ind-Hilbert spaces and Conformal field theory

This paper introduces a metric-dependent variant of factorization homology in conformally flat Riemannian geometry, defining conformally flat disk algebras as functors to ind-Hilbert spaces and proving that their left Kan extensions yield symmetric monoidal invariants that reproduce sphere partition functions of conformal field theories, with explicit constructions for $d>2$ derived from unitary representations of $\mathrm{SO}^+(d,1)$ .

Yuto Moriwaki2026-04-23🔢 math-ph

A Total Lagrangian Finite Element Framework for Multibody Dynamics: Part I -- Formulation

This paper presents a Total Lagrangian finite element framework for finite-deformation multibody dynamics that integrates compact kinematics, a deformation-gradient-based formulation, and a systematic constraint-construction machinery to model collections of deformable bodies under various loads, contacts, and material models.

Zhenhao Zhou, Ganesh Arivoli, Dan Negrut2026-04-23🔢 math-ph

Quantum $f$ -divergences via Nussbaum-Szkoła Distributions in Semifinite von Neumann Algebras

This paper extends the established result that quantum $f$ -divergences equal classical $f$ -divergences of Nussbaum-Szkoła distributions from the specific case of bounded operators on a Hilbert space to the general setting of normal states on any semifinite von Neumann algebra.

Theodoros Anastasiadis, George Androulakis2026-04-23⚛️ quant-ph

On non-relativistic integrable models and 4d SCFTs

This paper establishes a correspondence between the generalized Schur indices of 4d $N=2$ and $N=1$ superconformal field theories and the eigenfunctions of non-relativistic integrable models, such as the elliptic Ruijsenaars-Schneider and Inozemtsev systems, thereby deriving new mathematical identities and extending these relationships to various classes of SCFTs.

Rotem Ben Zeev, Anirudh Deb, Hee-Cheol Kim, Shlomo S. Razamat2026-04-23⚛️ hep-th

On Uniqueness of Mock Theta Functions

This paper develops a resurgent approach to uniquely continue mock theta functions across their natural boundaries by representing Mordell-Appell integrals as Laplace transforms of resurgent functions, thereby establishing a canonical continuation that singles out a distinguished family of these functions for orders 3 and 5.

Ovidiu Costin, Gerald V. Dunne, Ali Saraeb2026-04-23🔢 math-ph

Predictivity and Utility of Neural Surrogates of Multiscale PDEs

This paper critically examines the limitations of neural surrogates for multiscale partial differential equations, arguing that their success is often confined to low-dimensional manifolds and that fundamental issues like spectral bias and irreversible information loss from coarse-graining prevent them from reliably generalizing to genuinely chaotic scenarios, while suggesting that their true value lies in specific hybrid approaches and improved reporting standards.

Karthik Duraisamy2026-04-23🔢 math-ph

Graph-theoretic determination of massless modes in latticized theory-space models

This paper introduces a graph-theoretic method that determines the number and localization of massless fermion modes in latticized theory-space models by analyzing the maximum matching and Dulmage-Mendelsohn decomposition of bipartite graphs representing mass terms, providing a parameter-independent tool for systematic model construction.

Ketan M. Patel2026-04-23⚛️ hep-ph

Determining metrics from the scattering map of the time-dependent Schrödinger equation

This paper establishes that for a specific class of time-dependent metrics, the scattering maps of two Schrödinger operators differ by a compact operator if and only if the metrics are related by a diffeomorphism pull-back.

Qiuye Jia2026-04-23🔢 math-ph

Mathematical analysis of transverse EM field concentration for adjacent obstacles with nonlocal boundary conditions in the quasistatic regime

This paper provides a rigorous mathematical analysis of transverse electromagnetic field concentration between adjacent obstacles under quasi-static conditions, establishing sharp gradient blowup rates and demonstrating how nonlocal boundary conditions and wave frequency mitigate field enhancement to extend classical theories for nanophotonic device design.

Yueguang Hu, Hongjie Li, Hongyu Liu2026-04-23🔢 math-ph

Quantitative Direct Sampling for Initial Acoustic Sources

This paper introduces a novel quantitative direct sampling method using spacetime integral-based indicator functions to uniquely and accurately reconstruct initial acoustic sources from time-dependent wave measurements, demonstrating its robustness and efficiency through numerical experiments.

Xiaodong Liu, Xianchao Wang2026-04-23🔢 math-ph

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