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 a coordinate-free probabilistic framework for determinantal point processes on compact complex manifolds by rigorously defining scalar determinants for line-bundle-valued Bergman kernels, proving that finite-dimensional spaces of sections generate such processes, and deriving transfer principles that convert analytic asymptotics into probabilistic limit theorems.
This paper critiques the drawbacks of the standard bra-ket formalism and introduces a new, versatile representation-free scheme that supports both one-space and dual-space interpretations while facilitating practical calculations.
This paper establishes a unified framework for demonstrating strong illposedness in high-regularity Sobolev spaces for various quasilinear dispersive equations by analyzing the interplay between degenerate dispersion in the principal term and the failure of the Takeuchi--Mizohata condition in the subprincipal term, utilizing a robust energy- and duality-based method.
This paper proposes an explicit, oracle-free quantum framework that utilizes Schrödingerisation and efficient block-encoding to simulate general linear PDEs with Robin boundary conditions, inhomogeneous terms, and variable coefficients, achieving polynomial scaling in grid points and exponential advantages in spatial dimensions to overcome the classical curse of dimensionality.
This paper promotes the global symmetry of the Schwarzian derivative to a local gauge symmetry by constructing a gauge-invariant analogue of the Schwarzian derivative through a composite field method, thereby enabling the study of topological sectors and locally invariant couplings in two-dimensional gravity contexts.
This paper advances the exact-WKB formalism for general one-dimensional potentials by analyzing spectral transitions across sectors via complexification, deriving exact median quantization conditions and trans-series structures for asymmetric triple-well and tilted double-well systems, and establishing transformation rules for genus-1 resurgence data that clarify the link between path integrals and exact-WKB methods.
This paper reformulates the Tolman-Oppenheimer-Volkoff equations for static, spherically symmetric perfect-fluid stars within the semi-tetrad formalism as a covariant first-order dynamical system, enabling a geometric analysis of stellar structure through autonomous flows in phase space for both linear and general equations of state.
This paper demonstrates that Abelian -duality on ALE spaces transforms the Maxwell partition function from a scalar into a vector-valued boundary state composed of theta-function blocks, which exhibit modular covariance and encode higher-form symmetry data, thereby establishing ALE spaces as chiral building blocks that glue to reproduce standard closed-manifold partition functions.
This paper introduces MARUT, a scalable, GPU-accelerated high-order CFD framework featuring adaptive mesh refinement and finite-rate chemistry capabilities, designed to deliver high-fidelity simulations of compressible and reacting flows across subsonic to hypersonic regimes on exascale supercomputing architectures.
This paper establishes a generalized Minkowski theorem for constant-curvature Lorentzian spaces by proving that four non-trivial holonomies uniquely reconstruct a strictly convex tetrahedron in de Sitter or anti-de Sitter space under specific closure and convexity conditions, while also characterizing the resulting polar-dual projective tetrahedra and recovering classical Euclidean and hyperbolic reconstruction results in the spacelike sector.