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 demonstrates that universal quartic modifications to relativistic dispersion relations emerge generically from deformation-quantized phase spaces under minimal kinematical assumptions, a result confirmed through three independent mathematical frameworks: Fedosov-Berezov quantization, spectral geometry, and topos theory.
This paper establishes new curvature inequalities and rigidity results for constant mean curvature surfaces in Riemannian manifolds and spacetime constant mean curvature surfaces in Lorentzian geometry, demonstrating that these properties hold under weaker stability conditions and leading to flatness or Euclidean rigidity in the equality cases.
This paper provides a stable homotopy theoretical proof that the tenfold way classification of topological phases remains robust under weak interactions by constructing geometric definitions of weakly interacting time evolution operators and demonstrating that their associated spectra deformation retract to the standard and spectra.
This paper reviews how viewing two-dimensional Einstein field equations as an integrable system enables the derivation of exact solutions through Wiener-Hopf matrix factorisation, highlighting recent interdisciplinary advances in operator theory and complex analysis that yield explicit gravitational solutions and new solution-generating methods.
This paper examines rank-one complex crystallographic reflection groups to establish their connection with Seiberg-Witten integrable systems for Minahan-Nemeshansky SCFTs of type , providing a compact geometric description of the associated elliptic fibrations and deriving their quantum spectral curves as Fuchsian ODEs.
This paper investigates the conditions for strict positivity of entropy production in Quantum Reset Models, deriving analytical criteria for both combined Lindbladians and tri-partite systems with weak coupling, and validating these theoretical findings through explicit expressions and numerical simulations.
This paper establishes effective quenched linear response for non-uniformly expanding random dynamical systems with non-i.i.d. compositions, enabling the proof of parameter differentiability for the CLT variance and annealed linear response through applications to sufficiently mixing base maps and various one- and higher-dimensional examples.
This paper introduces a robust discrete formulation for computing the three-dimensional winding number of smooth maps to using -gaps, offering both a practical unmodified flux for fine grids and a modified flux that strictly guarantees integer quantization even in the presence of degeneracies.
This paper establishes a novel connection between topological entanglement and number theory by introducing a -deformed Witten zeta function within 3d Chern-Simons theory, demonstrating that the large- limit of Rényi entropies for torus link complements converges to values determined by classical Witten zeta functions, which admit a geometric interpretation via symplectic volumes of moduli spaces of flat connections.
This paper proves that single -weighted -Hurwitz numbers with internal faces, including monotone Hurwitz numbers and map enumerations on non-oriented surfaces, are computed by refined topological recursion on a rational spectral curve, thereby establishing that their generating functions analytically continue to rational curves and enabling the computation of correlators for Gaussian, Jacobi, and Laguerre -ensembles.