math-ph papers | Gist.Science

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.

🔢 mathematics

Digital Beam Pattern Optimisation for the GRAO 32-m Telescope: A Comparative Analysis of FIR Filter Design Methods

This paper presents a digital signal processing framework that adapts finite-impulse-response (FIR) filter design methods to optimize the beam pattern of the 32-m Ghana Radio Astronomy Observatory telescope, successfully suppressing sidelobes and cross-polar leakage to enhance its polarimetric precision and suitability for high-dynamic-range radio astronomy applications.

Theophilus Ansah-Narh, Nia Imara, Benedicta Woode, Emmanuel Proven Adzri2026-06-23

⚛️ quantum physics

On a Central Limit Theorem and Sanov's principle for quantum neural networks

This paper establishes a Central Limit Theorem and Sanov's principle for the fluctuations of a Mixture of Experts generated by quantum neural networks trained via gradient flow, demonstrating that these fluctuations satisfy a linear transport equation while the network converges to a limit function governed by the neural tangent kernel.

Anderson Melchor Hernandez2026-06-23

🌀 nonlinear sciences

Geometric Structures of Pseudo-Sonic Curves in Self-Similar Solutions of the Euler Equations for Potential Flow

This paper rigorously analyzes the geometric structures of pseudo-sonic curves in two-dimensional self-similar solutions of the Euler equations for potential flow, proving that these curves are necessarily circular arcs under specific conditions and establishing $C^{2,\alpha}$ regularity for shock reflection-diffraction problems with non-uniform incoming flows.

Gui-Qiang G. Chen, Mikhail Feldman, Xin Gao, Wei Xiang2026-06-23

🔢 mathematics

Heat Kernel and Resurgence

This paper investigates the resurgent structure of short-time heat kernel asymptotics on real analytic Riemannian manifolds by formulating an infinite-dimensional Picard-Lefschetz framework that connects alien operators to complex geodesic data, a proposal which is validated through a test case on the hyperbolic plane.

Si Li, Yong Li, Xinxing Tang2026-06-23

⚛️ high-energy theory

Holonomies and Boundary Symmetries in the Discrete Warped Chern-Simons Gravity

This paper proposes a discrete warped Chern-Simons gravity framework for three-dimensional warped AdS holography, demonstrating that boundary monodromies derived from ordered link holonomies serve as fundamental gauge-invariant observables that characterize physical sectors and reproduce warped black hole entropy and WCFT structures in the continuum limit.

H. T. Özer, Aytül Filiz2026-06-23

🔢 mathematics

Vafa-Witten Equations and Conformal Geometry

This paper establishes geometric and analytic constraints on closed 4-manifolds admitting nontrivial Vafa-Witten solutions, including new inequalities relating the Yamabe constant to the self-dual Weyl tensor, sharp volume bounds for positive Einstein manifolds, a correspondence between stable flat connections on 3-manifolds and $S^1$ -invariant solutions, and an energy gap theorem for the moduli space.

Teng Huang, Pan Zhang2026-06-23

🔢 mathematics

Electromagnetic Characterization of Magnetic Bar: Case of Square Cross-Section Shape

This paper presents a complete two-dimensional theoretical model for the electromagnetic behavior of square-section magnetic bars under sinusoidal loading, deriving exact mathematical expressions for key parameters and introducing a new apparent permeability parameter that enables rapid magnetic steel characterization while bypassing the computational costs of Finite Element Analysis.

Taha El Hajji, Bruno Ricardo Marques, Lars Sjöberg2026-06-23

🔢 mathematics

Level lines of the Gaussian free field and $c=1$ degenerate conformal blocks

This paper establishes that the crossing probabilities of level lines for both the continuum and metric graph Gaussian free fields with piecewise constant boundary data are determined by specific $c=1$ degenerate conformal blocks and ratios of fused $\mathrm{SLE}_4$ partition functions, which satisfy higher-order BPZ equations and correspond to conformal blocks labeled by generalized Dyck paths subject to monotonicity constraints.

Alex Karrila, Eveliina Peltola, Lukas Schoug2026-06-23

🔢 mathematics

Singular barriers and quartic integrability breaking in the TTW system

This paper demonstrates that a symmetric quartic deformation of the Tempesta-Turbiner-Winternitz system is non-integrable for small coupling due to the absence of a second independent first integral near a phase-locked orbit, while also showing that the system's singular barriers suppress chaotic transport without restoring integrability at finite coupling.

Adrian M. Escobar Ruiz, Miguel E. Gómez Quintanar, Lidia Jiménez-Lara, Jaume Llibre2026-06-23

🔢 mathematics

Minimum Virtual Proper Time and Finite Mass--Charge Matching in QED

This paper proposes a finite-proper-time formulation of QED that maintains exact gauge covariance and unitarity while yielding finite vacuum polarization and a calculable anomalous magnetic moment correction, resulting in a specific on-shell electron mass prediction without the need for renormalization.

Mustafa Bakr2026-06-23

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math-ph

Digital Beam Pattern Optimisation for the GRAO 32-m Telescope: A Comparative Analysis of FIR Filter Design Methods

On a Central Limit Theorem and Sanov's principle for quantum neural networks

Geometric Structures of Pseudo-Sonic Curves in Self-Similar Solutions of the Euler Equations for Potential Flow

Heat Kernel and Resurgence

Holonomies and Boundary Symmetries in the Discrete Warped Chern-Simons Gravity

Vafa-Witten Equations and Conformal Geometry

Electromagnetic Characterization of Magnetic Bar: Case of Square Cross-Section Shape

Level lines of the Gaussian free field and c=1c=1c=1 degenerate conformal blocks

Singular barriers and quartic integrability breaking in the TTW system

Minimum Virtual Proper Time and Finite Mass--Charge Matching in QED

Level lines of the Gaussian free field and $c=1$ degenerate conformal blocks