3366 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 presents a unified approach to constructing the Hermitian vector and canonical components of the momentum operator in 3D Euclidean space with general curvilinear coordinates by defining momentum as mass times velocity via the Heisenberg equation of motion, a method first illustrated with polar coordinates before being generalized.
This paper utilizes the Desnanot–Jacobi determinant identity to derive a simple determinantal representation for the widths of admissible correlation intervals in homogeneous one-dimensional random fields, thereby recovering and contextualizing previous results by Schneider and Hartlap within the framework of classical Toeplitz determinant theory.
This paper employs a Riemann–Hilbert approach to demonstrate that the initial boundary value problem for the sine-Gordon equation on the right half-line is uniquely determined by initial data alone, whereas the problem on the left half-line requires additional boundary data to be well-posed.
Building on the work of Deift and Zhou, this paper analyzes the long-time asymptotics of the autocorrelation function for the transverse Ising chain at the critical magnetic field via the Riemann-Hilbert problem, refining previous results by determining the subleading growing term.
This paper develops the notion of spaces over dg manifolds and establishes an equivalence between the category of transitive algebroids and that of spaces, while also constructing a faithful functor between them, with both mappings detecting weak equivalences.
This paper addresses the validation of stochastic system reconstruction from noisy data by demonstrating the limitations of standard deterministic metrics and proposing a threshold-free, two-step exploratory test, while acknowledging constraints imposed by system degeneracy, non-identifiability, and intrinsic stochastic features.
This paper investigates the zeros of independent and identically distributed Gaussian Laurent series on an annulus, demonstrating that their zero point process forms a permanental-determinantal point process characterized by weighted Szegő kernels and exhibiting specific symmetries and interpolation properties in the limit as the annulus shrinks to the unit disk.
This paper establishes that the diffusive scaling limit of a finite system of mutually avoiding long clusters in subcritical 2D FK-percolation converges to a system of non-intersecting Brownian bridges (Brownian watermelon), while also providing asymptotic estimates for connection probabilities and large cluster occurrences in related percolation models.
This paper proves the weak convergence of the power iteration method and the Rayleigh quotient for matrices with finite Levi-Civita field entries under a specific eigenvalue dominance condition, extends these results to Puiseux series, and provides a Python implementation.
This paper introduces the concept of -twisted restricted conformal blocks on a three-pointed twisted projective line, establishes their isomorphism to -twisted correlation functions and intertwining operators, and applies these results to derive a twisted version of the Fusion Rules Theorem.