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 presents a self-contained, combinatorial approach using Schur-Weyl duality and symmetric group character theory to derive simple closed-form expressions for all power moments of the von Neumann entropy of a random pure quantum state, offering an alternative to traditional random matrix theory methods.
This paper employs phase space deformation quantization using Weyl quantization and the Moyal star product to construct explicit Wigner distributions for Taub and Kantowski-Sachs cosmological models, thereby resolving factor ordering ambiguities and formal convergence issues while recovering standard wave functions expressed as modified Bessel functions.
This paper analyzes the four-dimensional Palatini-Cartan gravity model through various geometric-covariant formalisms, deriving its field equations, gauge symmetries, and Noether currents while employing multisymplectic, polysymplectic, and Dirac-Hamiltonian frameworks to characterize its momentum maps, constraint structures, and instantaneous Hamiltonian formulation.
This paper defines and studies log conifold transitions for index-two Fano threefold pairs, demonstrating that their global deformation theory is unconditionally unobstructed due to boundary geometry, which allows for the independent lifting of local node smoothings to construct new non-Kähler threefolds with analyzed Picard groups and Hodge theory.
This paper proposes a variational approach using extended two-variable Rayleigh quotients on admissible cone pairs to establish Rayleigh-type minimax principles for characterizing selected real spectral values of non-selfadjoint operator pencils with singular weights, thereby extending classical finite-dimensional approximation methods and providing stability guarantees, error estimates, and spectral certificates in settings where standard selfadjoint theory is unavailable.
This paper introduces a new cumulant-based quantum relative Rényi functional derived from the cumulant-generating function of the quantum relative surprisal operator, establishing its fundamental properties and demonstrating that a regularized version of this functional vanishes if and only if quantum states commute, thereby offering a novel characterization of non-commutativity and a conjectured monotonicity under commutativity-preserving channels.
This paper investigates boundary conditions in GiMmsy's instantaneous formulation of field theories, demonstrating that they induce a sector structure in the state space and lead to a novel definition of boundary symmetry groups, which for electromagnetism reduces to the global gauge group even when accounting for flux superselection sectors in Yang-Mills theory.
This paper presents a generic algorithm to decompose the transfer-matrix space of classical 2d lattice models with Temperley-Lieb face interactions into simple modules, enabling the analysis of topological operator actions and the computation of modular transformations for irreducible characters at primitive roots of unity.
This paper reviews the collaboration that established the first rigorous proof of the hydrogen molecule's stability in quantum mechanics, while also examining related issues such as symmetry breaking, stability domains of Coulombic few-body systems, and applications to exotic hadrons.
This paper derives a macroscopic thermodynamic theory for nematic liquid crystals by applying Chapman-Enskog expansions and constrained maximization to a kinetic model with BGK-type collisions, thereby generalizing existing inviscid theories to include viscous, thermal, and spin-diffusive effects for both compressible and incompressible fluids.