2563 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 derives a normal form for the simplest Lagrangian singularity arising from the projection of Hamilton-Jacacobi solutions onto space-energy, which is then utilized to construct asymptotic solutions for semiclassical equations when the energy corresponds to a critical value on the Lagrangian manifold.
This paper derives explicit, finite-sum formulas for discrete space-time wave kernels on regular trees in terms of - and -Bessel functions, providing convolution representations for solutions and analyzing their asymptotic behavior across large distances, times, and tree degrees.
This paper rigorously proves that the critical partition function of the Ising model coupled to 2D gravity converges to the -function of the string equation by utilizing a steepest-descent analysis of a Riemann-Hilbert problem associated with biorthogonal polynomials, thereby confirming long-standing conjectures by Douglas, Shenker, Brézin, Kazakov, Gross, and Migdal.
This paper demonstrates that the macroscopic fluctuation theory for a multispecies symmetric simple exclusion process on an infinite line constitutes an integrable system of Landau–Lifshitz type, allowing the derivation of the current cumulant generating function and conditioned density profiles via inverse scattering methods, ultimately revealing that the generating function depends on a single scalar variable and coincides with the single-species result regardless of the number of particle species.
This paper introduces a shell-based shortest-path anisotropy statistic for graph discretizations of black-hole geometries, demonstrating that this measure exhibits a stable radial organization strongly correlated with the logarithmic Kretschmann profile across various black-hole families, thereby serving as a curvature-sensitive diagnostic distinct from universal pointwise curvature scalars.
This paper presents a novel 5D UV completion for a class of Argyres-Douglas theories by embedding them into the renormalization group flow of 5D SCFTs on , utilizing the (-)Painlevé/gauge theory correspondence to compute BPS partition functions and analyze the phase diagram, with explicit results provided for the SCFT and its limit to the H AD theory.
This paper presents heuristic Euler-style computations that derive explicit expressions for the regularized infinite products of Gauss and Eisenstein integers and primes, extending the methodology used to evaluate the product of all natural primes.
This paper demonstrates that by selecting appropriate boundary conditions for the Laplacian, an ideal Bose gas in the thermodynamic limit can support an arbitrary number of Bose-Einstein condensates described by arbitrary harmonic functions.
This paper analytically and numerically investigates three non-Hermitian random matrix universality classes (A, AI, and AII) by characterizing their complex edge statistics through spacing ratios and nearest-neighbour distributions, revealing varying degrees of level repulsion consistent with a 2D Coulomb gas description and confirming universal cubic repulsion in the small-argument limit.
This paper investigates the geometry of classical trajectories in separable two-dimensional polynomial potentials, distinguishing between the global superintegrability of harmonic oscillators and the particular, trajectory-dependent superintegrability of anharmonic oscillators where closed nonlinear Lissajous orbits arise only under specific resonance conditions.