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.

🔬 mesoscale physics

Localization phase diagram of the Hexagonal Lattice with irrational magnetic flux

This paper establishes the exact localization phase diagram of the Hofstadter model on a hexagonal lattice with irrational magnetic flux by applying Avila's global theory to a two-by-two transfer matrix, revealing three distinct phases (extended, localized, and critical) without mobility edges, a finding subsequently validated by renormalization group theory and numerical fractal dimension analysis.

Qi Gao, Shuo Zhang, Wei Chen2026-08-05

🔢 mathematics

The $q$ -extension of iterated integrals and nested sums in quantum field theory

This paper constructs $q$ -extensions of special functions and nested sums arising in perturbative quantum field theory, deriving their differential and difference equations to address calculations involving $q$ -deformed commutation relations.

J. Blümlein, A. M. Gavrilik, O. Mykhailiv, C. Schneider2026-08-05

⚛️ high-energy theory

BRST quantization of Carroll-Weyl gauged null strings

This paper demonstrates that the BRST quantization of null strings with extended Carroll-Weyl gauge symmetry leads to an anomaly-free theory only under mutually incompatible dimension constraints ( $D=27, 6, 4$ ), proving that no single target-space dimension allows for a consistent highest-weight representation of the full three-constraint system, unlike the standard $D=26$ result obtained from the truncated BMS subsector.

Sarthak Duary, Sourav Maji2026-08-05

🌀 nonlinear sciences

Ramp, Plateau, and Wormholes without Averaging, and Hyper-non-perturbative Structures in Gravity

This paper proposes that universal signatures of quantum chaos, such as spectral ramps, plateaus, and wormholes, emerge as macroscopic smooth structures within microscopic data via a smooth filter projection rather than through ensemble averaging, thereby establishing a dual connection between a minimal Gutzwiller-like structure in holographic systems and hyper-non-perturbative gravitational objects like wormhole condensates.

Hong Liu2026-08-05

🔬 mesoscale physics

Nonlocality-induced critical-length hierarchy from non-Hermitian competition

This paper demonstrates that long-range hoppings in non-Hermitian coupled chains fundamentally reorganize the competition between skin accumulation and hybridization, replacing the conventional logarithmic critical-length law with a new hierarchy of algebraic and scale-covariant scaling regimes driven by nonlocal mechanisms.

Mengjie Yang, Alexander N. Poddubny, Ching Hua Lee2026-08-05

🔢 mathematics

Odd elasticity in a three-link microswimmer: feedback equivalence, global controllability, and the cost of non-reciprocity

This paper demonstrates that odd elasticity in a three-link microswimmer preserves its geometric controllability and nilpotent structure while solely modifying the energy cost of maneuvers, thereby enabling strictly cheaper reorientations and pure rotation at isotropic drag without requiring a non-reciprocity threshold.

Rossella Attanasi, Gaetano Napoli, Marta Zoppello2026-08-05

🔢 mathematics

Topological Recursion and Quantum Path Signatures

This paper introduces a non-commutative Laplace transform that converts path functionals into tensor series, enabling the derivation of a non-commutative spectral form for quantum path signatures and their subsequent expansion via topological recursion into a hierarchy of integral equations.

Inês Aniceto, Thomas Cass, Samuel Crew2026-08-05

🔬 condensed matter

Two dimensional inhomogeneous classical systems at criticality

This paper demonstrates that slowly varying inhomogeneous deformations of two-dimensional critical classical lattice models, such as the Ising and six-vertex models, are effectively described by conformal field theory in curved space, enabling the determination of underlying metrics and the calculation of phase boundaries like the arctic curve.

Jean-Marie Stéphan2026-08-05

🔢 mathematics

AKSZ Descent on Manifolds with Ordinary Corners

This paper develops a rigorous facewise formulation of the classical AKSZ construction on manifolds with ordinary corners by organizing codimension- $r$ data over the entire face poset to establish a total-complex theorem for defect cancellation, explicitly verifying these properties in four-dimensional BF theory and providing a reduction criterion for constructing strict corner theories from singular data.

Cristian Anghel2026-08-05

⚛️ general relativity

A generalization of the Fredenhagen-Haag derivation of Hawking radiation for a class of Vaidya space-times

This paper generalizes the Fredenhagen-Haag derivation of Hawking radiation to a class of Vaidya space-times by establishing a two-sided detector-response inequality through quantitative estimates on massless scalar fields, thereby demonstrating convergence to the standard thermal form under asymptotic stationarity while addressing the limitations of finite-mass evaporation scenarios.

Felipe Dilho Alves2026-08-05

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math-ph

Localization phase diagram of the Hexagonal Lattice with irrational magnetic flux

The qqq-extension of iterated integrals and nested sums in quantum field theory

BRST quantization of Carroll-Weyl gauged null strings

Ramp, Plateau, and Wormholes without Averaging, and Hyper-non-perturbative Structures in Gravity

Nonlocality-induced critical-length hierarchy from non-Hermitian competition

Odd elasticity in a three-link microswimmer: feedback equivalence, global controllability, and the cost of non-reciprocity

Topological Recursion and Quantum Path Signatures

Two dimensional inhomogeneous classical systems at criticality

AKSZ Descent on Manifolds with Ordinary Corners

A generalization of the Fredenhagen-Haag derivation of Hawking radiation for a class of Vaidya space-times

The $q$ -extension of iterated integrals and nested sums in quantum field theory