🔢 Category

math-ph

3262 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.

🔢 mathematics

On two differing geometric descriptions of the passage from microscopy to macroscopy in Markov diffusion theory

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.

Dalton A R Sakthivadivel2026-07-31
🌀 nonlinear sciences

Hamiltonian formalism for nonlinear Schrödinger equations

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.

Ali Pazarci, Umut Can Turhan, Nader Ghazanfari, Ilmar Gahramanov2026-07-30
🔢 mathematics

Symplectic Isomorphism Between Strong-Coupling Criticality and Finite-Strain Bifurcation

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.

Yu-Xin Xie2026-07-30