2656 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 constructs 3+1D and 2+1D Hamiltonian lattice models for Weyl fermions and Dirac cones that evade no-go theorems by utilizing exact, not-on-site chiral symmetries—specifically a Ginsparg-Wilson analog and an Onsager algebra—to protect gaplessness and generate global anomalies even in the absence of crystalline translations.
This paper establishes a quantum energy inequality for non-commutative quantum field theories by constructing deformed operator combinations that provide a rigorous lower bound on averaged energy density, thereby ensuring the theory's stability and physical consistency.
This paper introduces a Homothetic Gauge Theory based on a Homothetic Hodge de Rham framework, which utilizes a dilaton field to generate scale-covariant interactions that successfully regularize the divergent self-energy of a point charge, rendering both its electric field and total energy finite at the origin.
This paper formalizes a classification of three distinct types of local parent Hamiltonians that share a given quantum state as an exact eigenstate, rigorously deriving the complete set of such Hamiltonians for the state to reveal its role as a Quantum Many-Body Scar and establishing general constraints for product and short-range-entangled states.
This paper establishes a rigorous formulation of umbral theory within the context of formal power series with complex coefficients by defining the umbral operator on a subalgebra of analytically convergent series, utilizing Gevrey classification and Borel-Laplace resummation to validate divergent identities, and applying this framework to introduce new Gaussian trigonometric functions and a "Gaussian Fourier transform."
This paper simplifies the calculation of group character averages in a Gaussian matrix model by deriving generic sum rules that express arbitrary traces as convolutions of a single Laguerre polynomial, despite the complexities introduced by extended Laguerre polynomials in the matrix entries.
This paper characterizes the limiting geometry of numerical ranges for fundamental non-Hermitian random matrix ensembles, demonstrating that elliptic Ginibre and chiral variants converge to ellipses while non-Hermitian Wishart matrices and products of multiple elliptic Ginibre matrices form non-elliptic envelopes.
This paper establishes a unified algebraic framework using the meta Racah algebra to study finite families of Racah-type orthogonal polynomials and biorthogonal rational functions, identifying them as overlap coefficients that naturally yield their orthogonality relations and bispectral properties.
This paper establishes the precise late-time oscillating and decaying tails of charged scalar fields on near-extremal Reissner--Nordström spacetimes and proves the existence of asymptotic instabilities along future null infinity and the event horizon using purely physical-space methods without assuming smallness of the scalar field charge.
This paper establishes annealed central limit theorems for finite pattern counts in disordered quantum trajectories under summable mixing and trace-norm forgetting conditions, demonstrating that Gaussian fluctuations persist for admissible initial states and universally for all initial states in the perfect-measurement regime.