3324 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 analyzes zero-modes in a one-loop semi-classical Yang-Mills theory in 3+1 dimensions, demonstrating that they arise from gauge redundancy and, through proper gauge fixing with a bosonic ghost term and zeta-function regularization, yields a finite effective theory that reproduces the known one-loop beta-function.
This paper presents a group-theoretic interpretation of the periodic table using the Lie algebra , demonstrating how its weight diagram and root system naturally explain period doubling, spin splitting, and the inclusion of antimatter through the projection of a four-dimensional 24-cell onto two isomorphic subalgebras.
This paper introduces a novel method using approximate stochastic localization to prove a weak Poincaré inequality for the Sherrington-Kirkpatrick model at , thereby demonstrating that Glauber dynamics with a warm start efficiently samples its Gibbs measure.
This paper constructs localized approximate eigenfunctions for Hamiltonians modeling aperiodic crystals, demonstrating that under specific assumptions on the associated periodic operator family, these functions yield energy estimates with a controlled error of order for small .
This paper develops a covariant reconstruction framework in teleparallel gravity to derive specific functional forms of the gravitational Lagrangian for Kantowski--Sachs geometries sourced by Chaplygin and polytropic fluids, utilizing nonlinear matter conservation laws to reverse the standard reconstruction strategy and identify viable anisotropic cosmological and black-hole-interior branches.
This paper presents exact, assumption-free analytical formulas for the evolution operators of four time-dependent Hamiltonians relevant to quantum spin batteries by employing a novel combination of -algebra, path-sums, and Omega calculus, thereby enabling the recovery and extension of existing approximations and providing explicit exact formulas for Floquet Hamiltonians at all orders.
This survey paper presents a rigorous mathematical theory for quantum filtering equations in infinite-dimensional mixed-state systems, resolves a longstanding open problem in their derivation, and explores their applications to feedback control, quantum dynamics, and mean-field games through propagation of chaos limits.
This paper establishes that the lower edge of the appropriately scaled Laguerre beta-ensemble converges to the process as when the parameter satisfies and , thereby completing the classification of its edge scaling limits through operator-level convergence proofs and coupling arguments.
This paper proposes a generalized definition of temperature for isolated quantum many-body systems out of equilibrium by locating non-stationary states within a family of regular states compatible with their energy-coherence structure, thereby replacing the principle of maximum entropy with a principle of minimum discrimination information and extending the framework to subsystems via induced local thermodynamic structures.
This paper establishes the unconditional stability and convergence of a mixed finite element discretization for coupling continuum and discrete diffusion models, demonstrating its effectiveness through numerical examples and its utility in solving diffusive problems with incomplete data.