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 investigates the moduli space of multi-fractional instantons on a twisted by demonstrating that 't Hooft's constant field strength solutions constitute the entire moduli space only when , whereas for , they represent a measure-zero subset surrounded by non-constant, non-abelian solutions, a finding that resolves a recent puzzle and is validated through analytical, numerical, and lattice comparisons.
This paper demonstrates that the density of two-level atoms can be uniquely reconstructed from scattering measurements of entangled two-photon states by utilizing a quantum field theory model that links source-to-solution maps with nonlocal partial differential equations.
This paper investigates the capillary-driven retraction of a highly viscous liquid sheet in the limit of large Ohnesorge and aspect ratios, deriving a reduced heat-equation model with a single dimensionless parameter that reveals distinct retraction regimes—including early-time growth, a Taylor-Culick intermediate phase for long sheets, and late-time decay—through asymptotic matching of thin-film and tip-flow dynamics.
This paper establishes the norm resolvent convergence of magnetic Schrödinger operators with regular potentials to those with singular -interactions supported on networks (such as graphs or domain boundaries) under minimal assumptions allowing for complex-valued coefficients, while also discussing the resulting spectral implications.
This paper presents a geometric, structure-preserving semi-discrete formulation of Maxwell's equations in two and three dimensions using discrete exterior calculus, which maintains the continuous theory's intrinsic structures and yields an explicit general solution for the system on a two-dimensional combinatorial torus.
Motivated by critical planar percolation, this paper establishes that the probability of a planar Brownian motion containing two disjoint subpaths connecting the -neighborhood of its starting point to a macroscopic distance decays asymptotically as as approaches zero.
This paper constructs universal characteristic identities and explicit invariant projectors for split Casimir operators in tensor products involving defining and specific Cartan power representations across all simple Lie algebras (except ), expressing these results in terms of Vogel parameters to derive universal dimension formulas.
This paper characterizes the most general forms of input-output indefiniteness in bidirectional quantum devices by establishing a hierarchy of higher-order transformations built from bistochastic channels, which encompasses both indefinite local directions and indefinite global causal orders within a time-symmetric quantum framework.
This paper establishes a novel recurrence relation for the real-valued spectral moments of the Bures-Hall ensemble using Christoffel-Darboux formulas, which is then applied to rigorously derive the average von Neumann entropy and quantum purity, confirming recent conjectures by Ayana Sarkar and Santosh Kumar.
This lecture note outlines the proof strategy by Huang, McKenzie, and Yau (2024) for establishing the Ramanujan property and edge universality in random regular graphs, focusing on the derivation of self-consistent equations and microscopic loop equations.