3190 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 the Yang-Mills gradient flow drives multiply wound SU(2) center vortices toward an Abelian core with winding reduced modulo two by revealing that while the vortex core spreads diffusively, unstable tachyonic modes grow to unwind the excess topological charge, leaving only the fundamental vortex as a stable, marginally bounded fixed point.
This paper derives explicit formulas for the leading third and fourth cumulants of smooth linear statistics in a general -dimensional Coulomb gas by utilizing shape derivatives of the Dirichlet energy and the deformation of the equilibrium droplet, thereby extending previous two-dimensional radial results to non-radial settings and providing rigorous proofs for specific cases.
This paper proves a spatial symmetry invariance theorem for three-dimensional Navier-Stokes equations, demonstrating that traditional Direct Numerical Simulations fail to preserve this symmetry due to numerical noise rather than physical instability, thereby challenging the ergodicity assumption in turbulence theory and revealing fundamental flaws in current computational fluid dynamics benchmarks.
This paper utilizes Schur-Weyl duality to fully classify the subspaces within tensor-power spaces that support quantum private broadcasting by identifying conditions under which the collective Haar twirl acts as a replacement channel, while also characterizing how privacy and design properties are preserved when reducing the number of recipients.
This paper introduces a novel method using a parabolic-hyperbolic formulation and spectral solver to construct hyperboloidal initial data with direct analytic control over asymptotic charges, demonstrated by explicitly generating data for a spinning black hole with prescribed Bondi energy and angular momentum.
This paper establishes a -algebraic framework for generalized stabilizer codes on non-compact manifolds of arbitrary dimensions, characterizing their complete ground-state spaces through isotropic subgroups and proving the existence of unique frustration-free ground states with spectral gaps for Lagrangian models.
This paper reports the construction of thousands of holomorphic N=1 superconformal field theories with minimal Witten index for various central charges, including c=288, by leveraging ternary codes, AI-assisted searches, and symmetric orbifold techniques to overcome computational barriers and address open questions regarding the 576-periodicity of the TMF spectrum.
This paper presents an abstract formulation of the formal theory of partial differential equations within synthetic differential geometry, designed to generalize traditional frameworks to enhanced contexts like super-geometry and higher stacky geometry in order to facilitate the covariant geometric pre-quantization of locally variational field theories.
This paper establishes magnetic Hardy inequalities with singular integral weights, analyzes their local and global optimality through detailed examples, and applies these findings to derive spectral estimates for magnetic Schrödinger operators.
This paper constructs the nontrivial, isometry-covariant measure on arbitrary compact 3-dimensional Riemannian manifolds as an invariant probability measure of a singular stochastic partial differential equation, utilizing a novel renormalization approach based on microlocal and harmonic analysis to derive universal constants independent of the manifold geometry.