2548 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 introduces a novel diagrammatic technique in Quantum Electrodynamics that ensures infrared finiteness for inclusive cross sections and scattering matrices directly at the diagram level, eliminating the need for the standard cancellation of infrared divergences.
This paper provides an elementary analytical derivation showing that the charge density profile of a vortex core in a weak-coupling superconductor exhibits sign-alternating oscillations due to the inefficiency of screening at large momentum transfer, which prevents extended states from fully compensating the non-zero bound-state charge.
This paper applies a reciprocal transformation to link an integrable extension of the mKdV equation to a novel nonlinear evolution equation with a source term, and subsequently utilizes Ermakov-Painlevé II symmetry reduction to derive exact solutions for a class of associated Stefan-type moving boundary problems.
This paper constructs and analyzes a new family of mixed-type multiple orthogonal polynomials on the unit circle associated with a generic-rank matrix weight that generalizes Bessel-like systems, providing explicit hypergeometric formulas, recurrence relations, and a Christoffel factorization for their banded recurrence matrix.
This paper establishes a spectral and probabilistic theory for arbitrary finite-bandwidth Markov transition matrices by utilizing ordered positive bidiagonal factorizations to derive explicit formulas for transition probabilities and first-passage laws without requiring reversibility, while characterizing these systems through mixed-type multiple orthogonal polynomials and specific stochastic experiments.
This paper constructs a spectral triple for the twisted fuzzy torus using a Dirac operator defined by commutators and anticommutators, and investigates the resulting Connes spectral distance by establishing a reciprocal Pythagorean theorem, analyzing the diagonal nature of optimal elements for diagonal states, and exploring the relationship between conformal twists and spectral distances.
This paper introduces a noise-resilient, polynomial-time quantum approximation scheme (FPRASq) for constrained optimization that leverages geometry-informed guarantees and a novel Heavy-Hitter QAOA variant to achieve provable performance on NP-hard problems, demonstrating that quantum advantage in this context stems from generating superior sampling distributions rather than classical post-processing.
This paper establishes a unified deformation framework that lifts (2+1)-dimensional integrable systems, specifically the anisotropic KP and isotropic NNV equations, to higher-dimensional hierarchies with closed-form Lax pairs, while simultaneously generating new reciprocal Harry-Dym-type integrable systems and revealing how the spatial symmetry of the parent equation governs the properties of its deformations.
This paper classifies the conditions under which braid group representations arising from the Katz-Long-Moody construction factor through Hecke and Temperley-Lieb algebras, demonstrating that, with one exception, the factorization through Hecke algebras depends solely on the eigenvalues of the free-group part rather than the construction parameter.
This paper resolves a longstanding open problem in continuous variable quantum information by proving that the entanglement of formation for all two-mode Gaussian states equals their Gaussian restriction, a result derived from a sharp affine relation between entanglement and a generalized Einstein-Podolsky-Rosen observable that holds for arbitrary pure two-mode states.