1515 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 demonstrates that the statistics of chaotic dynamical systems can be predicted by mapping them to periodic differential operators, using a Fibonacci-tiling-based nonlinear recursion to derive explicit formulas that reveal how the system's clustering near critical values corresponds to van Hove singularities in the operators' densities of states.
This paper rigorously proves that Cayley's first hyperdeterminant serves as a legitimate entanglement measure for -qudit states by demonstrating that its magnitude is an LU-invariant, LOCC-monotonic quantity that vanishes on separable states and specifically detects genuine full -level GHZ-type entanglement.
This paper presents a well-conditioned, second-kind boundary integral equation for time-harmonic electromagnetic scattering by composite dielectric objects, achieved by extending the classical Müller formulation via the global multitrace method and Stratton-Chu representation, and solved efficiently using a Petrov-Galerkin discretization with Rao-Wilton-Glisson and Buffa-Christiansen functions.
This article commemorates the centennial of Erdal İnönü's birth by reviewing his life and institutional contributions while using the geometric analogy of a sphere flattening into a plane to explain his celebrated İnönü-Wigner contraction and its significance for modern physics.
This paper investigates the King function as a radial kernel for shifted Gaussian distributions by establishing its connection to the Laguerre hierarchy, deriving its governing differential equation and spectral representation via unitary equivalence to a free radial Schrödinger operator, and proving its utility as a dense, non-orthogonal basis for approximation theory alongside derived integrability and moment criteria.
This paper analyzes perturbations of strongly coupled Yang-Mills plasma by demonstrating that while classical spectral truncation methods are limited by convergence boundaries, an exact WKB analysis combined with Seiberg--Witten theory provides a systematic framework to resum quasinormal modes, yielding an accurate spectrum that remains valid from the large wave number regime all the way to zero.
This paper constructs -extensions for iterated integrals and associated nested sums arising in perturbative quantum field theory calculations, demonstrating that while these extensions generally preserve the underlying Hopf algebra structure and map into the same function space polynomially in , they lead to higher transcendental functions specifically in cases involving square-root valued alphabets or central binomials.
This paper introduces a censored stochastic six-vertex model, demonstrating that its blocking measure stochastically dominates the system at all times to control second-class particles, a result established through connections to Iwahori--Hecke algebras and the use of parabolic Kazhdan--Lusztig -polynomials as both explanatory tools and intertwining kernels.
This paper rigorously proves the existence of long-range order in the chirally charged fermion-mass bilinear for a class of two-dimensional Euclidean lattice Gross-Neveu models with even flavor numbers by utilizing reflection positivity, chessboard estimates, and Peierls-type arguments to establish a non-perturbative connection between the lattice theory and large- mean-field predictions across various discretizations.
This paper establishes that for diagonalizable non-Hermitian Hamiltonians with real spectra, the biorthogonal Gibbs functional satisfies the Kubo-Martin-Schwinger (KMS) condition if and only if the system is quasi-Hermitian, thereby providing a metric-free characterization of quasi-Hermiticity and proving that the resulting KMS states cannot be simply deduced from their Hermitian counterparts via similarity transformations.