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

Maximal subalgebras in the three exceptional simple finite-dimensional Lie superalgebras

This paper resolves the previously open problem of classifying maximal graded subalgebras for the three exceptional simple finite-dimensional Lie superalgebras $\mathfrak{osp}_a(4|2)$ , $\mathfrak{ag}(2)$ , and $\mathfrak{ab}(3)$ by enumerating their applicable $\mathbb{Z}$ -gradings and providing explicit descriptions of their maximal subalgebras, while also identifying a missing case in the general theory of graded subalgebras for vectorial Lie superalgebras of depth greater than one.

Dimitry Leites, Oleksandr Lozhechnyk2026-10-05

🔢 mathematics

Discriminating Lindbladian Dynamics

This paper establishes the fundamental limits of discriminating quantum Markovian dynamics by characterizing the optimal error exponent as the maximal instantaneous increase in quantum relative entropy and demonstrating that temporal resolution serves as a critical resource, enabling perfect discrimination with zero type-I error in certain quantum regimes where classical strategies fail.

Robert Salzmann, Ludovico Lami, Martin B. Plenio, Susana F. Huelga2026-10-05

🔢 mathematics

Modified logarithmic Sobolev inequality for 1D non-commuting Hamiltonians

This paper establishes the first modified logarithmic Sobolev inequality for finite-range, non-commuting Hamiltonians on 1D chains, proving that heat-bath dynamics and related Gibbs samplers achieve rapid mixing with times of order $\mathcal{O}(\log n \cdot \log(n/\epsilon))$ by combining weak quasi-factorization, decay-of-correlation estimates, and a uniform conditional local gap.

Ángela Capel, David Pérez-García, Matteo Scandi2026-10-05

🔢 mathematics

Complete Factorial Asymptotics and Integrable Structure of Generalized Charlier Recurrence Coefficients

This paper establishes the complete factorial asymptotics of the recurrence coefficients for generalized Charlier polynomials by proving their connection to the recessive solution of a discrete Bessel equation via a discrete Painlevé II parametrization and independently verifying these results through a sector decomposition of the associated Hankel determinants.

Mahouton Norbert Hounkonnou2026-10-02

⚛️ high-energy theory

Constructive Neural Network Field Theory: $\phi_2^4$ in Finite Volume

This paper introduces constructive neural network field theory to rigorously realize finite-volume scalar $\phi^4_2$ as a limit of network measures by organizing fields into momentum shells and proving that, for sufficiently fast-growing widths, the ultraviolet and infinite-width limits commute to recover the standard $\phi^4_2$ measure.

Samuel Frank2026-10-02

🔢 mathematics

Gaugino condensates in $\mathcal{N}=1$ super-Yang-Mills Theory on Eguchi-Hanson space

This paper investigates gaugino condensates in $\mathcal{N}=1$ $SU(N)$ super-Yang-Mills theory on Eguchi-Hanson space using instanton methods, demonstrating how fractional topological charge and boundary spectral asymmetry modify the calculus to yield specific condensate values that reproduce flat-space results for $SU(2)$ while revealing distinct non-perturbative structures for higher-rank groups.

Mohamed M. Anber2026-10-02

🔢 mathematics

Supermoduli spaces are non-projected in every genus $g\geq 3$

This paper proves that for every genus $g \geq 3$ , the moduli superstack of smooth unpunctured super Riemann surfaces is non-projected and non-split because its primary obstruction is nonzero in both algebraic and holomorphic settings.

Mauricio Corrêa, Ron Donagi, Simone Noja2026-10-02

🔢 mathematics

Endpoint Mapping Properties of Wave Operators for Schrödinger Operators in Dimensions $n\ge3$

This paper establishes the endpoint mapping properties of low-energy wave operators for Schrödinger operators in dimensions $n \ge 3$ , demonstrating that in four dimensions a zero-energy resonance obstructs $L^1$ boundedness, while in all dimensions $L^\infty$ boundedness in the presence of a zero-energy eigenvalue is equivalent to the vanishing of specific moments of the potential-weighted eigenfunctions.

Han Cheng, Changxing Miao, Xiaohua Yao2026-10-02

🔢 mathematics

Dissipation-Enabled Operator-Norm Locality Bounds for Bose-Hubbard Hamiltonians

This paper demonstrates that introducing local dissipation, such as on-site photon loss, to the Bose-Hubbard model restores uniform operator-norm Lieb-Robinson bounds independent of the initial state's boson occupancy, thereby enabling rigorous thermodynamic limits and efficient quantum simulation for open bosonic systems.

Marius Lemm, Tim Möbus2026-10-02

🔢 mathematics

Superintegrability of a resonant ghostly tri-Hamiltonian model: polynomial first integrals and transcendental completion

This paper establishes that a resonant three-dimensional Hamiltonian with indefinite kinetic energy and tri-Hamiltonian structure is minimally superintegrable within polynomial and rational classes but achieves maximal superintegrability on a specific domain when a branch-free transcendental invariant is included, with these classical results successfully extended to the quantum regime via Weyl quantization.

Andreas Fring, Ian Marquette2026-10-02

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math-ph

Maximal subalgebras in the three exceptional simple finite-dimensional Lie superalgebras

Discriminating Lindbladian Dynamics

Modified logarithmic Sobolev inequality for 1D non-commuting Hamiltonians

Complete Factorial Asymptotics and Integrable Structure of Generalized Charlier Recurrence Coefficients

Constructive Neural Network Field Theory: ϕ24\phi_2^4ϕ24​ in Finite Volume

Gaugino condensates in N=1\mathcal{N}=1N=1 super-Yang-Mills Theory on Eguchi-Hanson space

Supermoduli spaces are non-projected in every genus g≥3g\geq 3g≥3

Endpoint Mapping Properties of Wave Operators for Schrödinger Operators in Dimensions n≥3n\ge3n≥3

Dissipation-Enabled Operator-Norm Locality Bounds for Bose-Hubbard Hamiltonians

Superintegrability of a resonant ghostly tri-Hamiltonian model: polynomial first integrals and transcendental completion

Constructive Neural Network Field Theory: $\phi_2^4$ in Finite Volume

Gaugino condensates in $\mathcal{N}=1$ super-Yang-Mills Theory on Eguchi-Hanson space

Supermoduli spaces are non-projected in every genus $g\geq 3$

Endpoint Mapping Properties of Wave Operators for Schrödinger Operators in Dimensions $n\ge3$