1605 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 generalizes Zhu's theorem on modular invariance to quasi-lisse vertex algebras by proving the holonomicity of conformal blocks over the moduli space of bundles and showing that their flat sections are spanned by trace functions, thereby establishing that the dimension of the space of conformal blocks for affine vertex algebras at admissible levels equals the number of admissible weights.
This paper introduces HyperPrecision, a Mathematica package that enables high-precision numerical evaluation of multivariate hypergeometric functions and their Laurent expansions by automatically constructing Pfaffian systems, reducing them to ordinary differential equations along a contour, and solving them via the Frobenius method to overcome convergence limitations in physics and mathematics applications.
This paper establishes a partial reversal of the Simon-Lieb inequality for Bernoulli percolation in dimensions , which leads to the uniform boundedness of Duminil-Copin and Tassion's quantity and provides a concise derivation of key near-critical estimates and sharp bounds on the critical one-arm probability.
This paper establishes a convergence framework for the Airy line ensemble based on the pole evolution of meromorphic functions satisfying stochastic differential equations, which is then used to prove the universality of this ensemble as the edge scaling limit for various continuous-time processes including Dyson Brownian motions, Laguerre, and Jacobi processes.
This paper resolves the long-standing ghost instability problem in the Pais-Uhlenbeck model by leveraging Lie symmetries and its Bi-Hamiltonian structure to construct positive-definite formulations and equivalent first-order systems, while also analyzing how interaction terms typically disrupt this underlying structure.
This paper establishes an -loss version of Pólya's conjecture for bounded Lipschitz domains by providing explicit quantitative estimates for the Weyl law remainder without relying on Neumann eigenvalues, thereby reducing the conjecture to a computational problem and identifying broader classes of domains, including irregular shapes and strip-tiling domains, that satisfy the conjecture or even exhibit stronger eigenvalue bounds.
This paper derives exact, explicit formulas for the average relative entropy between random quantum states drawn from Hilbert-Schmidt and Bures-Hall ensembles, utilizing unitary integral factorization to complement existing asymptotic results.
This study utilizes a semi-analytical model to map the dynamical structure of Earth's co-orbital region, revealing that horseshoe orbits dominate the phase space with significant inhomogeneities and varying levels of chaos, which implies that a large fraction of the Earth co-orbital asteroid population remains undiscovered and poses potential challenges for planetary defense.
This paper constructs explicit -adapted Hilbert spaces using representation theory to decompose the geodesic flow on a closed hyperbolic surface into a damped harmonic oscillator and a transverse wave group, thereby providing a unified spectral framework that explicitly links classical geodesic dynamics, Ruelle resonances, and the Laplace spectrum through a dynamical derivation of the Selberg trace formula.
This paper presents exact analytical solutions for the gravitational collapse of a massive scalar field coupled with perfect fluid and dissipative matter in a conformally flat spacetime, demonstrating that such configurations evolve asymptotically without forming shell-focusing singularities within finite proper time, even when exhibiting effective exotic matter behavior.