1695 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 geometrical formulation of nonlinear electrodynamics without birefringence, demonstrating that linear perturbations evolve on a field-dependent optical metric, thereby enabling the application of quantum field theory techniques and facilitating the development of analogue models using nonlinear metamaterials.
This paper establishes that a Berwald spacetime is locally concave if and only if its flag curvature is nonnegative in timelike directions, while also providing a new characterization of nonnegative flag curvature through the convexity of future or past capsules.
This paper establishes the global well-posedness and proves the global-in-time convergence, including optimal rates of , of the hyperbolic linear sigma model to its mean-field limit on the two-dimensional torus, while also demonstrating the convergence of their respective invariant Gibbs dynamics.
This paper performs a group classification of a class of (1+2)-dimensional linear partial differential equations for Asian option pricing, identifying an eight-dimensional Lie invariance algebra that allows transformation to the Kolmogorov equation and facilitates the construction of invariant exact solutions through symmetry reduction.
This paper elucidates the connections between auxiliary field formulations of four-dimensional duality-invariant electrodynamics and two-dimensional integrable sigma models by demonstrating that their relationships are governed by Legendre transformations and field redefinitions, thereby establishing correspondences between specific formalisms and extending known families of integrable deformations.
This paper establishes a Poisson Hamiltonian formulation for the optimal control of mechanical systems on Lie groupoids, demonstrating that symplectic leaves of the dual Lie algebroid serve as the natural reduced phase spaces and proving the equivalence between variational and Poisson Hamiltonian approaches under regularity conditions.
The paper proves that for any local Hamiltonian on a spin chain at finite temperature, there exists a finite entanglement length such that removing an interval of that size renders the remaining left and right half-chains separable.
This paper proposes entropy-stable numerical schemes for the generalized Lagrange multiplier (GLM) reformulation of the Chew, Goldberger & Low (CGL) plasma flow equations, demonstrating through numerical results that this approach significantly improves the control of magnetic field divergence compared to the standard CGL model.
This paper establishes a general framework for continuous deterministic data assimilation in semilinear parabolic equations using a nudged model driven by partial observations, proving global well-posedness and exponential convergence of the approximating solution to the reference system under suitable conditions, thereby extending the approach to diverse systems like Allen-Cahn, Cahn-Hilliard, Sellers-type energy balance, and bidomain equations.
This study demonstrates that while heavy-tailed -stable jump processes induce anomalous super-diffusive transport in turbulent flows, truncating or exponentially tempering these jumps suppresses long-range excursions and restores classical diffusive behavior.