3190 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 general definition of higher-form connections on principal -bundles within derived differential geometry by utilizing formal differentiation and integration to construct Atiyah -algebroids, thereby recovering known ech-Deligne cocycle notions and establishing connections to higher Courant algebroids with applications in higher gauge theory and supergravity.
This paper demonstrates that sequences of perfect t-embeddings for uniformly weighted generalized tower graphs satisfy the necessary rigidity assumptions to prove that the gradients of their height function fluctuations converge to the Gaussian free field.
This paper presents a probabilistic construction of the ultraviolet renormalization for the two-dimensional Sine-Gordon model on bounded convex domains, utilizing a martingale method refined with charge conjugation symmetries to establish existence for all particle activities and throughout the full subcritical range .
This paper constructs the scaling limit of a near-critical, length-weighted loop-erased random walk in two and three dimensions, demonstrating a phase transition in mutual absolute continuity with the classical limit and showing that while the curve becomes macroscopically space-filling as the boost increases, its Hausdorff dimension remains unchanged.
This paper extends the -function method for rational second-order ODEs to cases with non-Liouvillian first integrals by establishing a correspondence with linear differential equations, thereby reducing the decidability of Liouvillianity to classical algorithms and successfully recovering known equations like Airy and Bessel from high-degree examples.
This paper investigates the non-equilibrium density fluctuations of a one-dimensional stirring process with weak boundary dynamics, demonstrating that the limit is an Ornstein-Uhlenbeck process governed by Robin boundary conditions and relying on sharp bounds for space-time -functions derived in a companion article.
This paper presents an experimentally feasible implementation of a phase oracle as a reusable subroutine within the Measurement-Based Quantum Computation (MBQC) framework using cluster states, offering a transparent formulation of its measurement patterns and byproduct correlations that addresses the lack of explicit oracle construction in prior MBQC demonstrations of Grover's algorithm.
This paper generalizes Gordon's Theorem to arbitrary winding numbers by establishing a complete classification of minimizers for the Keplerian action functional with homogeneous potentials, proving that circular solutions lose local minimality below a specific threshold while collision-free minimizers exist above another, thereby resolving the previously open case for potentials with exponent and winding numbers .
This paper unifies diverse mathematical interpretations of the coefficients of bounded chain products—ranging from de Moivre's dice problem and spin multiplicities to constant-sum codes—by establishing a common notation, proving symmetry and log-concavity properties, and deriving explicit asymptotic expansions and limit behaviors for both equal and arbitrary bounds.
This paper derives exact analytical formulas for the variances of relative entropy over Hilbert–Schmidt and Bures–Hall ensembles for both independent and cross-ensemble random states, utilizing zonal polynomials and eigenvalue correlation functions to demonstrate the typicality of average relative entropy in limiting regimes.