2670 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 an algorithmic construction of a -graded differential variety that extends a given positively graded structure by incorporating an arborescent Koszul-Tate resolution in its negative part, utilizing explicit homotopy data to minimize homological computations and providing a concrete application to Lie-Rinehart algebras.
This paper generalizes the covariant quasilinear wave equation for the Riemann curvature tensor, originally established for Levi-Civita connections, to spacetimes with generic affine connections featuring torsion and nonmetricity, and analyzes its specific forms within Einstein spaces, teleparallel gravity, and Einstein-Cartan theory.
This paper extends the spectral theory of Markov chains beyond the classical birth-and-death setting by applying a spectral Favard theorem to chains with transition matrices admitting a positive stochastic bidiagonal factorization, thereby deriving Karlin-McGregor representations, establishing recurrence conditions, and characterizing stationary distributions and ergodicity through associated orthogonal polynomials and spectral measures.
This paper establishes a geometric mechanics framework using Euler-Poincaré reduction to derive 3-dimensional Eulerian equations of motion and Kelvin-Noether circulation conservation laws for self-gravitating barotropic fluids within the 3+1 ADM formulation of general relativity, thereby bridging relativistic hydrodynamics with Newtonian fluid dynamics and offering potential applications for numerical relativity.
This paper proposes a formal framework for a Lorentzian, -covariant noncommutative Kadomtsev–Petviashvili hierarchy constructed from Dirac-type operators and hypercomplex gauge fields, which describes integrable sectors of nonabelian gauge theories in dimensions.
This paper investigates the spectral properties and resonance behavior of the acoustic operator with piecewise constant coefficients by deriving a resolvent difference formula to establish a Limiting Absorption Principle and characterize the spectrum, while also providing analytic expansions for resonances in the asymptotic regime where the domain shrinks and material parameters vanish.
This paper proposes a quantum radar system utilizing a Born-Feynman path integrals approach with quantum dot-based entangled photon generation, microwave transmission, and cryogenically cooled superconducting detectors to achieve precise target detection through quantum correlation analysis.
This paper generalizes tetrahedron equations and their solutions by introducing -correspondences to accommodate additional parameters, rephrasing the equations in terms of Wronskian evolutions, and exploring underlying cohomological structures termed "quaternities" or "bibitorsors."
This paper establishes the existence of open parameter regions in the edge-2star model with hard constraints where entropy-optimal graphons are either unique and analytically varying or nonunique and symmetry-related, while also determining the boundaries of these regimes and proving foundational theorems linking optimal graphons to Boltzmann entropy.
This paper proposes using Noether's second theorem, rather than the first, to derive unique and physically consistent energy-momentum and spin currents for free massive Dirac particles, thereby resolving the ambiguities typically associated with pseudogauge transformations in relativistic spin hydrodynamics.