2669 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 investigates the analytical properties and presents an efficient Galerkin-based numerical solution using B-splines for the Bardeen-Cooper-Schrieffer equation describing unconventional superconductors with long-range power-law interactions on a -dimensional lattice, with specific results demonstrated for a nodal superconductor on a two-dimensional square lattice.
This paper proposes and validates a finite-element space discretization combined with implicit-explicit time marching to simulate salt crystallization in stone artifacts, extending previous one-dimensional models to higher dimensions while conducting sensitivity analysis, stability considerations, and convergence testing.
This paper introduces Feature-Enriched Kolmogorov-Arnold Networks (FEKAN), a parameter-efficient extension that enhances the computational efficiency, convergence speed, and predictive accuracy of existing KAN architectures through feature enrichment while maintaining their interpretability.
This paper establishes a Lorentzian equivariant index theorem for twisted Dirac operators on compact globally hyperbolic spacetimes with timelike boundaries, demonstrating that the equivariant index under APS boundary conditions follows the same fixed-point integral formula as in the Riemannian case through a novel reduction technique linking the equivariant index to spectral flow.
This paper extends classical edge-triangle Exponential Random Graph Models to inhomogeneous block-structured settings, establishing a large deviation principle and deriving a variational formula for the limiting free energy that, under ferromagnetic conditions, reduces to a scalar optimization problem and yields uniqueness and a law of large numbers for edge density under specific parameter constraints.
These Les Houches lecture notes, delivered in Summer 2024, provide an accessible, foundational introduction to the topological recursion framework, aiming to clarify its core concepts for readers encountering it across diverse fields like matrix models, string theory, and gauge theories without attempting to exhaustively detail every specific application.
This paper describes and classifies five-dimensional maximal supergravities with gauge groups contained in , uncovering a new family of theories and identifying their supersymmetric anti-de Sitter vacua as dual to superconformal phases of the M5-brane field theory.
This paper investigates the connection between amplituhedra and genus zero pairs within Brown and Dupont's mixed Hodge theory framework, demonstrating that while known positive geometries yield genus zero pairs, general amplituhedra can produce strictly positive genus pairs, thereby proving that genus zero is not a necessary condition for a space to be a positive geometry.
This paper establishes that Reshetikhin-Turaev link invariants arising from Chern-Simons theory can be recovered as trace maps on the factorization homology of a specific filtered -algebra constructed via BV quantization.
This chapter investigates the fundamental relationship between accuracy and robustness in classical and quantum classification algorithms under noisy and adversarial conditions by clarifying definitions, establishing theoretical trade-off conditions, and exploring implications for noise, adversarial perturbations, and future dynamical systems approaches.