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 demonstrates that exact WKB methods provide a powerful and systematically improvable framework for analytically computing the zero-damped mode spectrum of near-extremal Reissner--Nordström black holes with higher accuracy than previous studies.
This paper derives exact N-soliton solutions for the coupled negative first order Klein-Gordon equation under vanishing boundary conditions using the inverse scattering method via the Gelfand-Levitan-Marchenko equation, while also establishing its conservation laws, integrals of motion, and Hamiltonian structure through the zero-curvature representation.
This paper proposes a reciprocal tube tight-binding approximation method that utilizes translation-rotation transformations and reciprocal nanotubes to efficiently calculate the electronic band structures of armchair, zigzag, and chiral single-walled carbon nanotubes across all radius ranges, including those with significant curvature effects.
This paper rigorously analyzes the topological color code model on an infinite lattice using the -algebra framework and DHR theory to classify its anyon superselection sectors, demonstrate their equivalence to a double layer of the toric code, and characterize the system's thermal states.
This paper constructs helicity-conditioned statistical states for a Whitney-discretized electromagnetic field on a closed three-manifold, deriving explicit information-geometric properties such as Fisher information and relative entropy to characterize these states as conditioned inferences rather than dynamical equilibria.
This paper introduces a new class of alternative-mean trace functionals defined via operator monotone functions, proving that they constitute quantum divergences inducing the Bures–Wasserstein metric and satisfying sharp quadratic bounds relative to this metric.
This paper presents a representation-independent symmetric-Fock space formulation of the Boltzmann collision operator for Maxwell molecules, establishing a canonical lift-fusion structure that intrinsically explains the triangular hierarchy of Maxwell kinetics, recovers known spectra, and demonstrates that coordinate realizations can be chosen for computational economy without compromising the underlying abstract Fock formulation.
This paper demonstrates that incorporating Dirac delta interactions into quantum potentials via a discontinuous superpotential and self-adjoint extension imposes algebraic constraints that truncate and fix the number of bound states, thereby enabling the engineering of discrete spectra in systems like the harmonic oscillator and Rosen-Morse potential, while proving incompatible with Calogero-type singularities due to regularization breakdown.
This paper proves Conjecture 1.9 of Gabrielov-Novikov-Shapiro by demonstrating that any nonconstant restriction of a potential generated by point charges to a line possesses at most critical points, a sharp bound established through duality with an auxiliary planar potential and Morse theory.
This paper demonstrates that a one-dimensional fractional Ginzburg--Landau model with marginal dispersion () exhibits BKT-like correlation scaling and a finite-temperature transition, despite lacking the universal helicity modulus jump characteristic of the two-dimensional XY model.