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 a simplified proof demonstrating that the Newell-Whitehead-Segel equation yields a null solution by utilizing recent insights into convolution integrals to avoid complex nested calculations and confirming the result through alternative representations like expansions and Fujita-type solutions.
This paper investigates the limiting spectral distribution of a -deformed random unitary ensemble associated with the little- Laguerre weight, deriving a -deformation of the Marchenko-Pastur law that exhibits a phase transition at a critical value and establishing its convergence and large deviation properties through moment methods, equilibrium problems, and orthogonal polynomial asymptotics.
This paper unifies the Cartan and Weil models of equivariant cohomology with BRST quantization to establish a transparent analytic proof of the Atiyah--Bott--Berline--Vergne localization formula, demonstrating how gauge-fixing procedures naturally lead to equivariant Witten deformation and illustrating the framework through explicit computations on complex projective spaces.
This paper reformulates the operator product expansion of heavy conformal field theory correlators as a Stieltjes moment problem to derive two-sided bounds and saddle-point solutions corresponding to generalized free fields, ultimately applying these techniques to predict OPE coefficients for interacting double-twist operators in holographic theories.
This paper introduces a dual variational principle for Chern-Simons theory that overcomes the lack of coercivity in the original functional by constructing a bounded, lower semi-continuous dual action, thereby proving the existence of minimizers that constitute "variational dual solutions" to the theory's Euler-Lagrange equations.
This paper establishes an exact mathematical analogy between the fully nonlinear equations of ideal Field Dislocation Mechanics and ideal Magnetohydrodynamics, thereby suggesting the transferability of recent weak solution results and enabling the development of a dual variational principle for studying these systems.
This paper demonstrates a novel duality-based variational scheme that treats the inviscid Burgers equation in both conservation and Hamilton-Jacobi forms as degenerate elliptic problems, successfully generating approximate weak solutions and recovering specific entropy solutions through a time-marching algorithm utilizing dual-to-primal mappings and evolving base states.