2619 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 superintegrable realization of the Laguerre–Heun algebra by identifying it as the quadratic symmetry algebra of the two-dimensional Smorodinsky–Winternitz II system, which is separable in both Cartesian and parabolic coordinates.
This paper demonstrates that axisymmetric Willmore surfaces can be described by a first-order ordinary differential equation derived from two independent first integrals, thereby providing a convenient classification scheme for such surfaces.
This paper establishes a precise framework for distinguishing between energy-independent Wilson holonomies and energy-dependent spectral monodromies in spin-orbit rings, demonstrating how this separation enables the mapping of spin-orbit Hamiltonians to effective gauge connections to derive exact spectral quantization and transport properties in systems like graphene and Rashba-Dresselhaus rings.
This paper analyzes the coupled Riemann problem for compressible Euler equations with a stationary heat-flux discontinuity, demonstrating that non-uniqueness arises in Lax weak entropy solutions and establishing the existence and structure of unique admissible solutions under specific smallness conditions on the heat flux jump while identifying cases where no such solutions exist.
This paper revisits Jean-Marie Souriau's geometric quantization of the relativistic electron by proving key theorems to establish necessary symplectic and contact structures, ultimately deriving the Dirac equation, spin current conservation, and a systematic Kaluza-Klein-based construction of C, P, and T symmetries.
This heuristic paper extends the Laplace-Beltrami formalism, previously used to model gravitational wave energy from coalescing compact binaries, to a broader analysis of the Einstein field equations across zeroth, first, and second-order differential terms to evaluate its practicality and limitations in describing various general relativistic systems.
This paper establishes the local existence of weak solutions for time-dependent fractional Kohn-Sham equations in three dimensions with energy subcritical non-linearities, proves their global extension under specific energy control conditions, and demonstrates well-posedness for the case where the fractional parameter lies in using Strichartz estimates.
This paper derives and solves the Schwinger-Dyson and saddle point equations for type (0,1) random fuzzy geometries coupled to fermions or bosons, providing rigorous free energy and moment formulas in Gaussian cases that connect to the Hoppe and three-colour models.
This paper derives exact analytic quasi-stationary states for a massive scalar field in a dyonic Kerr-Sen black hole background using horizon-regular coordinates, revealing a quantized spectrum where positive-energy modes grow exponentially to destabilize the chronology-violating inner region, thereby supporting Hawking's chronology protection conjecture.
This paper establishes the long-time asymptotics for the focusing modified Korteweg-de Vries equation with finite-genus quasi-periodic initial data and discrete spectrum in a critical regime where stationary phase points coalesce with branch cut endpoints, revealing that the solution is uniformly approximated by a modulated algebro-geometric background and breathers governed by a Painlevé XXXIV parametrix.