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 derives exact solutions to the Schrödinger equation and continuum mechanics equations by applying a nonlinear Legendre transform to the continuity equation with a generalized Maxwell distribution as the momentum density, yielding explicit expressions for vector fields, density distributions, and potentials alongside a comprehensive physical analysis.
This paper establishes a nonperturbative framework using analytic continuation to reconstruct regular reduced dynamics from divergent time-local generators, revealing how such divergences signal the approach to noninvertibility and identifying early-time anisotropy signatures in open quantum systems like the spin-boson model.
This paper develops structure-preserving time integration schemes, including Boris-type and high-order symplectic methods, for magnetic Gaussian wave packet dynamics by reformulating the variational Dirac--Frenkel equations as a Poisson system, thereby ensuring the conservation of key invariants and providing rigorous error bounds uniform in the semiclassical parameter.
This paper presents a unified, rigorous microlocal sheaf-theoretic framework that generalizes the Maslov-WKB method to overcome caustic singularities and prove Bohr-Sommerfeld-Einstein-Brillouin-Keller quantization conditions for general semiclassical operators in one degree of freedom.
This paper demonstrates that the wavefunction of the universe for conformally coupled scalars in power-law FRW cosmologies satisfies a graphical coaction that reveals its complete analytic structure through acyclic minors of Feynman graphs, thereby reproducing known kinematic flows and simplifying the extraction of discontinuities across all particle multiplicities and loop orders.
This paper derives a nonlinear uncertainty principle for Lipschitz maps on Banach spaces, demonstrating that it generalizes and reduces to the classical Heisenberg-Robertson-Schrodinger uncertainty principle when applied to linear operators on Hilbert spaces.
This paper revisits the theory of multiplier modules of Hilbert C*-modules to establish their invariance under strong Morita equivalence, characterize the relationships between their associated operator algebras and duals, and demonstrate that while the extension of bounded module operators and functionals from a Hilbert C*-module to its multiplier module may fail to exist, any such existing extension is necessarily unique.
This paper computes various families of commuting elements in the matrix shuffle algebra of type , expected to be isomorphic to quantum toroidal , by expressing them as partial traces of products of -matrices with a lattice path interpretation, utilizing quantum toroidal algebra machinery and a new anti-homomorphism.
This paper establishes the continuum excursion decomposition of the two-dimensional critical XOR-Ising model by linking it to level sets of a Gaussian free field and proving that this decomposition emerges as the scaling limit of the discrete double random current model on the square lattice.
This paper formulates positive and negative flows of the Chen-Lee-Lee-Liu model and Burgers hierarchy using Riemann-Hilbert-Birkhoff decomposition, derives their soliton solutions and vertex operators via a dressing method for both zero and constant non-zero vacua, and introduces gauge-Bäcklund transformations to generate additional multi-soliton solutions through interactions with integrable defects.