2619 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 explicit conditions under which the successive Markovianisation of a positive Radon measure on continuous paths converges to measures satisfying the strong Markov property, demonstrating that translation-invariant measures on locally compact Polish groups fulfill these criteria within a specific set-theoretic framework.
This paper extends the theory of exterior differential systems to transitive Lie algebroids by establishing two versions of the Cartan-Kähler theorem and demonstrating their application to the invariant inverse problem of the calculus of variations.
This paper analyzes the solvability of a discrete nonlinear Schrödinger equation featuring a subcubic potential and specific forward/backward difference operators, assuming positive real parameters and a continuous potential function.
This paper proposes a non-Abelian gauge field framework based on hypercomplex ring formalism that introduces non-compact hyperbolic symmetries to double internal degrees of freedom, thereby enabling the description of bipartite gauge systems and field dissipation while utilizing a commutative ring to decouple algebraic structures and facilitate solutions to the equations of motion.
This paper derives the explicit free energy expansion up to the constant term for determinantal Coulomb gases in quadratic fields with a point charge, identifying the constant term with the Liouville action and utilizing a deformation framework combined with the foliation flow method to extend isotropic results to anisotropic settings.
This paper establishes that the occurrence of "magic relations" in Feynman integrals is intrinsically linked to the presence of higher-dimensional critical varieties, providing a practical computational test to detect these identities, count master integrals, and analyze their behavior under symmetries and cuts.
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.