3210 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 the concept of tagged vector spaces to mathematically formalize Dirac notation in quantum optics, demonstrating how the properties of tags and their extractors naturally yield commutation relations for ladder operators and a symplectic phase space, while extending to functional representations for spatiotemporal and spin degrees of freedom.
This paper addresses the inverse problem of identifying a time-dependent source coefficient in a one-dimensional heat equation with a spectral fractional Laplacian by reducing it to a Volterra equation, proposing a stable and convergent numerical scheme based on fractional matrix powers and Crank–Nicolson discretization, and demonstrating robust reconstruction performance even with noisy data.
This paper establishes that the universal local point processes of random matrix theory, specifically the and processes, are uniquely characterized by their respective bulk and edge loop equation hierarchies, thereby providing a direct pathway to proving universality by verifying these approximate equations.
This paper utilizes resurgence theory to demonstrate that the strong-coupling asymptotic expansion of the generating function for higher-genus Gromov-Witten invariants of the resolved conifold encodes both dual closed curve counts and contributions from relative Gromov-Witten invariants within the framework of logarithmic geometry.
This paper establishes the optimal anisotropic local law for sample covariance matrices in the proportional regime under the sole assumption of uniform quadratic-form concentration, thereby removing the restrictive higher-cumulant tensor assumptions required by previous work and extending the result to a broad class of distributions including log-concave vectors and deep random features.
This paper reformulates the linearized hard-sphere Boltzmann operator using Bargmann-Fock and coherent-state representations to explicitly separate angular and radial structures, thereby providing a constructive framework for analyzing its global spectral geometry, essential spectrum, and the emergence of quadratic continuum corridors via symmetry.
This paper establishes a geometric unification between the heavy top and the relativistic spinning particle by demonstrating that the latter is a Lorentzian analog of the former within the Euler-Poincaré reduction framework, where spacetime position acts as the advected quantity, thereby clarifying the effects of external fields and revealing how left-trivialized coordinates naturally select interaction Lagrangians that redefine the particle's mass through spin-field coupling.
This paper constructs five new families of -ary quantum maximum-distance-separable (MDS) codes with minimum distances exceeding by utilizing complements of unions of finite-field subsets to generate Hermitian self-orthogonal generalized Reed-Solomon codes, thereby achieving strictly larger minimum distances than several existing constructions for infinitely many odd prime powers .
This paper presents a large-scale numerical study of bulk correlation functions in the two-dimensional Abelian sandpile model across square, honeycomb, and kagome lattices using Wilson's algorithm and the Majumdar–Dhar bijection, confirming logarithmic conformal field theory predictions and providing the first systematic analysis for the kagome lattice alongside a new analytical derivation for its height-1 probability.
This paper establishes a unified combinatorial framework for canonical Bose and Fermi partition functions by utilizing symmetric-function and -ring identities to analyze how tensor factorizations of single-particle spectra determine many-particle statistics and product spectra.