3210 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 that every -dimensional canonical system with a positive semidefinite Hamiltonian satisfying possesses at least one nontrivial -integrable solution and that the space of all such solutions has a dimension of at most .
This paper computes all stringy invariants for -character varieties of free abelian groups and -Higgs bundle moduli spaces on abelian varieties, providing a direct proof of topological mirror symmetry for Langlands dual groups and establishing that symplectic resolutions of these moduli spaces exist only for groups of Dynkin types , , and .
This paper establishes the existence and universality of pure quasifree Hadamard states for the Klein-Gordon field on globally hyperbolic spacetimes with timelike boundaries by formulating a microlocal condition on the compressed future cone via a -wave-front set, thereby avoiding complex analysis on the manifold with corners and constructing the states through a propagation theorem and deformation argument.
This paper constructs a class of integrable chiral fermionic quantum field theories with spacetime-dependent interactions by utilizing a unitary two-body scattering matrix and characteristic coordinates to derive exact wavefunctions via discrete connections satisfying the Yang-Baxter equation and quantum Knizhnik-Zamolodchikov constraints, illustrated through a chiral Gross-Neveu realization.
This paper derives exact finite- integral representations and proposes the first microscopic two-time spectral kernels for the non-Hermitian Gaussian bulk classes , , and under Ornstein--Uhlenbeck evolution, revealing universal parametric correlations, spectral rigidity, and the role of eigenvector nonorthogonality in spectral diffusion.
This paper establishes that Haag duality in quantum spin systems is equivalent to the asymptotic vanishing of conditional mutual information, thereby linking the validity of duality for various geometric regions to specific entropic properties such as area laws and the vanishing of topological entanglement entropy.
This paper introduces the concept of reduction ideals to define a new class of reductions for integrable differential-difference equations, yielding finite-dimensional integrable systems in both commutative and noncommutative settings that enable the extension of reduced solutions to the original equations, as demonstrated through the Volterra hierarchy.
This paper investigates a 4-dimensional generalization of Lotka-Volterra predator-prey models, classifying them into integrable families that lead to unsustainable population dynamics and chaotic families that support long-term species coexistence, as evidenced by Lyapunov exponents and Poincaré surfaces of section.
This paper numerically validates the theoretical mechanism of subdiffusive transport in interacting disordered quantum chains by demonstrating that rare nonresonant regions, which act as insulating bottlenecks, persist with exponentially decaying but parametrically long survival probabilities across successive Schrieffer-Wolff scales, thereby confirming the physical relevance of rigorous constructive proofs at accessible system sizes.
This paper establishes a unified algebraic framework based on twisted multistate Perk--Schultz matrices and Lax operators to derive exact solutions for a broad class of hidden free fermion models, revealing their spectral organization and multiscale behaviors, including the resolution of the inhomogeneous free-fermions-in-disguise chain.