2563 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 introduces McMg, a learned phase-space multigrid preconditioner that encodes local wave information (amplitude, phase, direction, and scattering) into coarse-grid channels to efficiently solve high-frequency, heterogeneous Helmholtz equations with superior convergence and generalization compared to classical and existing neural baselines.
This paper proves that a system of particles interacting with two finite heat reservoirs via Kac-type collisions is well-approximated by dynamic Maxwellian thermostats for times shorter than , even when the reservoirs possess distinct temperatures and average velocities.
This paper establishes a connection between the Poisson bracket of Lagrangian field theory and algebras by demonstrating that a proposed symplectic structure yields the Peierls formula, interpreting the inverse relation between these structures via homological algebra, and applying these concepts to the complexities of -adic string theory.
This paper presents a consistent canonical quantization of General Relativity within a BRST-invariant framework around the Minkowski vacuum, demonstrating that classical spacetime geometries emerge as coherent states where the vanishing Hamiltonian constraint is realized as an expectation value, thereby enabling non-trivial time evolution for correlation functions and providing motivation for spontaneously broken supersymmetry.
This paper introduces a novel hybrid coupling framework that integrates non-intrusive Operator Inference reduced order models and high-fidelity full order models using the overlapping Schwarz alternating method, achieving up to 106x speedups in complex 3D solid dynamics simulations while maintaining high accuracy.
This paper establishes an invertible, isometric noncommutative Fourier transform for square-integrable wave functions on Lie groups that maps position space to a dual momentum space with noncommuting momenta, addressing normalization challenges from compact subgroups to derive a noncommutative Poisson summation formula essential for computing Wigner functions and path integrals.
This paper addresses the gap in modeling stiff forces in soft matter systems by providing a practical summary of constrained Brownian dynamics equations with "soft" constraints and a novel singular perturbation derivation that validates their use over relevant timescales, while also extending the framework to scenarios with spatially varying mobility.
This paper proves Anderson localization for Schrödinger operators on quantum graphs where the connectivity between vertices is governed by orbits of a subshift of finite type.
This paper establishes a novel connection between synthetic curvature bounds and the causal character of maximizers to prove that low-regularity inextendibility of spacetimes implies unbounded curvature, a result unattainable by classical methods that significantly strengthens previous findings.
This paper derives a generalized geodesic deviation equation in metric-affine gravity to demonstrate how torsion and nonmetricity introduce distinct, measurable corrections to tidal accelerations, offering a potential pathway for future direct detection of post-Riemannian spacetime features.