1694 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 introduces spectral Barron spaces within the framework of quantum harmonic analysis, establishes their fundamental properties such as completeness and continuous embeddings, and applies these results to prove the existence and uniqueness of solutions for a Schrödinger-type equation.
This paper introduces a novel mechanism called exceptional-bound (EB) band engineering that enables system-size-controlled topological transitions in non-Hermitian systems through unique critical scaling near exceptional points, distinct from the non-Hermitian skin effect and applicable to diverse experimental platforms.
This paper introduces the instrumental group algebra (IGA) as a Banach algebra framework for sequential quantum measurements, demonstrating that the time-dependent Kraus-operator density (KOD) evolves via a classical Kolmogorov equation and that combining instruments corresponds to convolution within the IGA, thereby providing a unified mathematical structure for observables that cannot be measured by orthogonal projections.
This paper investigates the Cauchy problem for a nonlinear damped Schrödinger equation involving the Riemann zeta function, establishing the uniqueness of distributional solutions, proving the existence of global solutions via regularization and compactness arguments, and demonstrating that solutions in the one-dimensional case vanish in finite time.
This paper establishes the theoretical framework for solving axial symmetric Navier-Stokes equations in a cylindrical topology by constructing a complete basis of harmonic 1-forms comprising Beltrami, anti-Beltrami, and closed components, thereby reducing the problem to a hierarchy of quadratic relations suitable for future optimization via Physics-Informed Neural Networks.
This paper clarifies the abstract geometrical formulation of thermodynamics on non-compact symmetric spaces used in Cartan Neural Networks by proving that only Kähler spaces support Gibbs distributions, explicitly characterizing their generalized temperature spaces via adjoint orbits, and demonstrating the equivalence between various information and thermodynamical geometries while establishing the covariance of these distributions under the full symmetry group.
This paper provides a learner-focused, methodical exposition on deriving the General Lagrangian Mean (GLM) and pseudo-Lagrangian equations for inviscid, incompressible, homogeneous fluids to describe the interactions between mean flows and waves.
This paper demonstrates that a canonical extension of generalized Dynkin diagrams generates families of Kac-Moody groups, such as the series relevant to string theory, which satisfy homological stability and exhibit emergent structures upon stabilization, utilizing homotopy decompositions of their classifying spaces.
This review paper demonstrates that spatial torsion in Metric-Affine Gravity induces non-linear quantum fluctuations affecting spinless degrees of freedom through the Stochastic Variational Method, revealing a competitive interplay with Levi-Civita curvature and a structural parallelism with information geometry.
This paper establishes global well-posedness in the critical energy space and proves almost periodicity in time for the half-wave maps equation on the one-dimensional torus by leveraging its integrable Lax pair structure to derive explicit solution formulae and a general stability principle that extends to matrix-valued cases and companion results on the real line.