2656 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 establishes a framework for defining self-adjoint realizations of 2d-dimensional canonical systems through symplectic geometry and Lagrangian boundary conditions, demonstrating their critical application in analyzing the spectral stability of traveling waves and solitons in nonlinear partial differential equations.
This paper demonstrates that pure SU(3) Yang--Mills theory on a punctured three-ball generates a finite, hadronic-scale spectral gap through a gauge-invariant quantum rotor mechanism driven by a Berry-shifted holonomy angle, thereby realizing "mass without mass" without introducing explicit mass terms or Higgs fields.
This paper generalizes the Peter-Weyl Theorem by demonstrating that functions on locally compact groups with large nontrivial compact open subgroups can be approximated by locally representative functions.
This paper presents a simple construction of algebro-geometric solutions to the Gelfand–Dickey hierarchy using an -type infinite ODE system and Dubrovin's method, while also deriving a formula for the -point function of the associated Riemann -function.
This paper establishes a hydrodynamic framework for force dipoles in compressible membranes with odd viscosity by deriving an exact Green tensor that reveals distinct dynamical regimes and chiral observables, such as transverse drift and relative motion, arising from the interplay of shear, compressional, and odd-viscous modes.
This paper investigates the irreducible components of fixed point sets within the -character variety of a genus two surface under finite group actions, utilizing the genus two DAHA to identify geometric transitions that yield novel candidates for symmetry-reduced moduli spaces in 4d SCFTs.
This paper derives WKB-asymptotic expressions for multipoint Virasoro conformal blocks in the comb channel on the sphere by applying the WKB method to the classical BPZ equation, validating the results against known exact solutions and AGT correspondence while demonstrating their utility for generalizing Zamolodchikov's elliptic recursion and numerically evaluating minimal string theory amplitudes.
This paper classifies differential operators between spaces of weighted densities in the superdimension setting, effectively superizing a previous result on modular forms and identifying open problems in the field.
This paper proposes a classical model of elementary particles where distinguishing between the center of mass and the center of interaction leads to a description of spinning particles whose dynamics, when the center of interaction moves at light speed, yield Dirac's equation upon quantization.
This paper introduces a comprehensive framework that unifies formal group theory and group entropies to create a flexible, infinite family of Mirror Descent optimization algorithms, featuring a novel "mirror duality" mechanism that adapts to diverse data geometries and statistical distributions while enhancing convergence and regularizer design in machine learning.