1677 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 develops a colored directed graph formalism to establish sharp operator norm bounds for partial traces of matrix tensors, demonstrating that their maximum values depend on the maximal number of directed cycles in associated graphs and applying these combinatorial results to extend asymptotic freeness concepts in multi-matrix random matrix theory.
This paper proves that for even levels, the Chern-Simons topological quantum field theory is naturally isomorphic to the Reshetikhin-Turaev TQFT constructed from the pointed modular category , establishing their equivalence as extended -dimensional theories for both closed 3-manifolds and bordisms with boundary.
This paper demonstrates that wave-particle complementarity is fundamentally reshaped by indefinite causal order, revealing a separation between spatial and causal resources that precludes a universal linear additive relation and necessitates the introduction of "causal coherence" to fully capture interference between alternative causal orders.
This paper derives and analyzes reduced bidirectional and unidirectional weakly nonlinear models for hydroelastic water waves coupled to a nonlinear viscoelastic plate, establishing local and global well-posedness results for these new nonlocal evolution equations.
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.