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 demonstrates that for two randomly chosen -dimensional observables, the set of classical states admitting a positive Kirkwood-Dirac representation is a minimal polytope of dimension , implying that almost no experimental configurations support such classical descriptions and highlighting the inherent nonclassicality of most quantum systems.
This paper resolves the incompatibility between two gauge-invariant accounts of the Abelian Higgs mechanism by demonstrating, through constrained Hamiltonian formalism and -algebraic analysis, that the mechanism involves the spontaneous breaking of physical global symmetry (which persists under boundary conditions) rather than local gauge symmetry, thereby establishing the Coulomb gauge as the preferred framework for a consistent gauge-invariant description.
This paper introduces a novel integrability-preserving discretization for differential equations with variable coefficients by developing an extended Rota algebra framework based on Laurent polynomials and utilizing categorical functors to unify continuous and discrete dynamical systems, thereby enabling the construction of integrable maps that share exact solutions and symmetry groups with their continuous analogues.
The paper demonstrates that the category of orthomodular posets forms a full coreflective subcategory of strong orthoposets by constructing a coreflector that preserves the underlying set and orthocomplementation while modifying the order, a result that also establishes a right adjoint functor from ortholattices to orthomodular posets.
This paper argues that physical theories with irregular nomic structure, characterized by ill-posed equations of motion and surplus representational capacity, are best analyzed through a category-theoretic framework where symplectic reduction is treated as arrow composition, thereby establishing equivalence between theories with isomorphic reduced state spaces and laying the groundwork for their quantization.
This paper establishes that the existence or non-existence of infinite clusters in bond percolation on infinite locally finite trees remains stable under specific quantitative perturbations of edge retention probabilities, with applications to the Erdős similarity conjecture for Cantor sets.
This paper investigates parent Hamiltonians for ergodic matrix product states (EMPS) defined by random tensors, demonstrating that under mild injectivity assumptions, these states serve as unique frustration-free ground states in the thermodynamic limit while establishing conditions for spectral gaps using the martingale method and illustrating scenarios where such gaps may or may not exist.
This paper derives an extended wave action model for equatorial chorus waves that identifies a Benjamin-Feir index threshold (BFI > 0.5) to predict the emergence of non-Gaussian, asymmetric frequency spectra primarily in the night and dawn sectors of the magnetosphere, providing a first-principles framework for threshold-based space weather modeling.
This paper challenges the conventional view of Lax pairs as strict structural certificates of integrability by demonstrating through five case studies and the Sparse Identification of Lax Operators (SILO) framework that compatibility conditions often underdetermine the representation, allowing "anomalous" or "fake" pairs to still generate full conservation hierarchies and thus revealing a more nuanced landscape than the binary distinction between true and fake Lax pairs.
This paper establishes a local linking theorem for relativistic action functionals by overcoming compactness challenges through a novel perturbative construction combining min-max geometry and Ekeland-Lasry regularization, thereby proving the existence of at least two non-constant solutions for the Lorentz force equation and the prescribed mean curvature operator in Minkowski space.