2656 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 establishes a direct analytical link between the eigenvalues of symmetric random matrices and their persistence diagrams via Morse theory, demonstrating that the resulting persistence entropy serves as a novel, high-performance spectral diagnostic for distinguishing universality classes and detecting spectral perturbations where traditional metrics fail.
This paper establishes that the fluctuations of periodically weighted Aztec diamond dimer models near their turning points, as the system size tends to infinity, converge to a marked GUE-corners process where independent Bernoulli marks encode the model's periodicity, a result proven via a double-contour integral representation of the inverse Kasteleyn matrix on a higher-genus Riemann surface.
This paper derives exact boundary four-point Green's functions for conformal loop ensembles with , providing explicit formulas for critical Bernoulli percolation and the FK-Ising model that confirm previous conjectures and reveal a logarithmic singularity, while also extending existing factorization results to all in this range.
This paper investigates averaged fundamental solutions of Laplace operators in arbitrary-dimensional Euclidean space using probabilistic kernels, deriving new representations for deformed solutions and their zero values while illustrating applications to renormalization in specific quantum field models.
This paper reviews the mathematical structure, physical origins, and diverse applications of completely monotone and Stieltjes functions in quantum field theory, highlighting their role in constraining scattering amplitudes, informing numerical bootstrap methods, and connecting to positive geometry.
This paper establishes the uniqueness of Gibbs measures and exponential ratio weak mixing for the supercritical loop O(1) and random current models on the hypercubic lattice () by introducing a novel exploration coupling of Pisztora's coarse-graining method to prove unique crossing events for conditional random-cluster measures.
This paper constructs and rigorously proves the properties of a hierarchy of rational solutions to the massive Thirring model, representing nonlinear superpositions of algebraic solitons via double-Wronskian determinants and characterizing their pole structures and slow scattering dynamics on the time scale.
This paper extends the enumeration of planar hypermaps with an alternating boundary to the general case, including Ising-decorated maps, by developing a new strategy involving the simultaneous elimination of two catalytic variables to derive algebraic equations and explicit rational parametrizations, thereby demonstrating that certain properties specific to the previously studied m-constellation case do not hold generally.
This paper extends the classification of gapped phases with categorical symmetries to include anti-unitary time-reversal symmetries by introducing Galois-real fusion categories over as the appropriate mathematical framework, enabling the classification of such phases via module categories and their realization as boundary conditions in a -enriched Symmetry Topological Field Theory.
This paper establishes a complete classification of Clifford quantum cellular automata on arbitrary metric spaces and qudits by identifying their stabilized group with the Witt group of a Pedersen–Weibel category derived from algebraic L-theory, thereby demonstrating that their classification depends solely on the large-scale coarse geometry of the underlying space.