3383 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 gauge transformations used to normalize non-linear connections in Joyce structures, as well as the resulting formal twistor Darboux coordinates, possess convergent Borel transforms, thereby establishing their resurgence.
This paper proposes a geometric model predictive control framework that uses Riemannian cubics on projective Hilbert space to generate smooth quantum trajectories while incorporating obstacle avoidance through potential functions and structure-preserving discretization.
This paper investigates how alternating the signs of frequencies for even and odd wavenumbers in nonlinear wave equations creates "staggered dispersions" that sustain bi-directional, drifting dispersive shocks with solitonic oscillations, leading to symmetrized dynamics, fractalization, and quantum revival effects.
This paper introduces "indivisible stochastic processes" and proves a theorem establishing a precise correspondence between these processes and unitarily evolving quantum systems, thereby offering a new first-principles formulation of quantum theory that explains its mathematical foundations and suggests novel applications for quantum computing.
This paper constructs a new algebraic linearization of the discrete periodic Toda flow using Mumford's description of the Jacobian and Gauss composition adapted by Cantor, revealing a novel integrality property that connects the flow to -adic number theory and the periodic box-ball system.
This paper extends the shielding effect previously discovered in soliton gases to deterministic breather gases for the focusing nonlinear Schrödinger equation by constructing an infinite-N limit where breathers uniformly fill a compact domain in the complex plane, resulting in finite breather solutions under specific conditions.
This paper presents a framework for the combinatorial quantization of 4d 2-Chern-Simons theory on a lattice by modeling extended Wilson surface operators on 2-graphs as measurable fields, demonstrating that their quantum 2-gauge symmetries form a Hopf category with a categorical quasitriangular structure known as cobraiding, thereby realizing the Baez-Dolan categorical ladder proposal.
This paper establishes that Calabi-Yau metrics on conifolds, their crepant resolutions, and their smoothings admit polyhomogeneous expansions near singularities by constructing approximate solutions via weighted Melrose-type blow-ups and gluing techniques, then proving the existence of exact solutions through a fixed point argument applied to the complex Monge-Ampère equation.
This paper demonstrates that neither polyconvexity nor true-stress-true-strain monotonicity alone guarantees physically reasonable behavior in isotropic hyperelasticity, suggesting that while their combination is a promising solution to Truesdell's Hauptproblem, no global strain-energy function satisfying both conditions has yet been identified.
This paper demonstrates that conformable semigroups do not constitute a genuinely new theory but are mathematically equivalent to classical -semigroups under a nonlinear time reparametrization, thereby proving that their chaotic and hypercyclic dynamical properties are identical to those of the corresponding classical systems.