2548 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 proves that among all measurable sets in the complex plane with a fixed area, the disc maximizes the Ky Fan norm of the Toeplitz operator with a characteristic symbol on the Fock space, thereby confirming a conjecture by Nicola, Riccardi, and Tilli and extending the classical Faber–Krahn inequality to general using techniques from quantum information theory.
This paper re-establishes the integrability of the hierarchy through diverse structural methodologies, including bi-Hamiltonian and Lie-Poisson frameworks, while demonstrating its relationship to the case via a flat limit and identifying its connection to the coadjoint orbits of for energy-dependent Schrödinger operators.
This paper constructs a central mathematical object that mediates between two distinct geometric descriptions of the transition from microscopic particle dynamics to macroscopic parabolic partial differential equations within Markov diffusion theory, utilizing a Fréchet manifold framework of probability densities on Riemannian manifolds to partially universalize this hierarchy.
This paper applies the Dirac-Bergmann formalism to derive Hamiltonian descriptions for second- and fourth-order nonlinear Schrödinger equations, demonstrating that while cubic and logarithmic second-order cases involve only primary constraints, higher-order dispersion necessitates secondary constraints to ensure consistent equations of motion.
This paper establishes conditions under which a specific system of partial differential equations involving Laplace–Beltrami, divergence, and gradient operators admits only trivial solutions on Riemannian manifolds with positive constant sectional curvature, a result motivated by applications in -form and mixed symmetry tensor gauge theories.
This paper strengthens no-go theorems for pointwise-defined quantum fields by demonstrating that weak continuity, combined with canonical commutation relations, microcausality, or Poincaré-invariant vacuum conditions, necessitates the vanishing of general spinorial fields on globally hyperbolic and Minkowski spacetimes.
This paper establishes a symplectic isomorphism between the infrared dynamics of strongly coupled scalar field theories and finite-strain bifurcation mechanics, enabling the derivation of a non-perturbative, first-principles rational scaling law for the 3D Ising anomalous dimension by mapping renormalization group flow to the spectral degeneration of a continuous Riccati-Lyapunov system.
This paper demonstrates that while the standard scalar quantum theory on a line with two origins is indistinguishable from the ordinary real line, the theory for spinors with a nontrivial spin structure detects the doubled origin through the necessity of specific boundary conditions at the singular point, revealing that the geometry alone does not uniquely determine the quantum transmission law.
This paper establishes universal bounds on the intersection numbers of BPS string generators in six-dimensional supergravity by combining Zariski decomposition with current algebra embeddings, thereby proving the finiteness of tensor charge intersections up to duality.
This paper derives the first explicit single-variable special function representation of the pair correlation function for the bulk limit of a beta-ensemble beyond the classical values of and $4$, specifically expressing it in terms of Bessel functions for the Sine process.