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

Remarks on "Further comments on "Rebuttal of "Refutation of "Comment on "Reply to "Comments on "A genuinely natural information measure" " " " " " "

This paper serves as a final, albeit reluctant, and satirical rebuttal by Z. Sommer and A. Winter against John Doe and Jean Roe's persistent criticisms of a previous refutation regarding a proposed "genuinely natural information measure." The authors clarify that the original work under discussion was authored solely by A. Winter, not by both Sommer and Winter, and present this April Fools' commentary as a humorous conclusion to the exchange.

Z. Sommer, A. Winter2026-04-01

🔢 mathematics

The Contextual Modal Logic of a Wigner's Friend Generalization

This paper argues that the logical inconsistency purportedly demonstrated by the Frauchiger-Renner Gedankenexperiment is resolved by applying the property of contextuality from the Kochen-Specker theorem, rendering the supposed contradiction logically inaccessible.

Felipe Dilho Alves, João Carlos Alves Barata2026-04-01

🔢 mathematics

Separable neighbourhood of identity in C $^{\ast}$ -algebras

This paper investigates the existence and size of separable neighborhoods around the identity in bipartite C*-algebras by reducing the problem to estimating completely bounded norms of contractive positive maps, thereby characterizing these neighborhoods via the algebra's rank and resolving a conjecture by Musat and Rørdam.

Mizanur Rahaman, Mateusz Wasilewski2026-04-01

🔢 mathematics

Ground state energy of the Bose--Hubbard model with large coordination number with a polaron-type quantum de Finetti theorem

This paper establishes the convergence of the ground state energy of the Bose-Hubbard model on graphs with large coordination number to a strong-coupling mean-field functional by developing and applying a novel "polaron-type" quantum de Finetti theorem tailored for tensor products involving bosonic Fock spaces.

Shahnaz Farhat, Denis Périce, Sören Petrat2026-04-01

🔢 mathematics

Fused K-operators and the $q$ -Onsager algebra

This paper introduces and studies fused K-operators of arbitrary spin within the framework of the alternating central extension of the $q$ -Onsager algebra, proving that they satisfy the spectral-parameter dependent reflection equation and providing explicit expressions for low-spin cases.

Guillaume Lemarthe, Pascal Baseilhac, Azat M. Gainutdinov2026-03-31

🔢 mathematics

Evolution of the Torsional Rigidity under Geometric Flows

This paper investigates the evolution of torsional rigidity under geometric flows by deriving specific bounds for Heisenberg spaces and homogeneous spheres under Ricci Flow, and establishing comparison inequalities with flat disks for strictly convex free-boundary hypersurfaces under Inverse Mean Curvature Flow.

Vicent Gimeno i Garcia, Fernán González-Ibáñez2026-03-31

🔢 mathematics

Differential system related to Krawtchouk polynomials: iterated regularisation and Painlevé equation

This paper establishes a connection between the recurrence coefficients of generalised Krawtchouk polynomials and the Painlevé V equation by demonstrating how iterative regularisation of their associated differential system yields polynomial systems and decompositions of birational transformations.

Galina Filipuk, Juan F. Mañas-Mañas, Juan J. Moreno-Balcázar, Cristina Rodríguez-Perales2026-03-31

⚛️ high-energy theory

Weak Hopf non-invertible symmetry-protected topological spin liquid and lattice realization of (1+1)D symmetry topological field theory

This paper introduces a generalized cluster ladder model that utilizes weak Hopf symmetry to construct a lattice realization of (1+1)D symmetry topological field theory, providing an exact solution via weak Hopf tensor network states for arbitrary fusion category symmetries.

Zhian Jia2026-03-31

🌀 nonlinear sciences

Effective Velocities in the Toda Lattice

This paper establishes a law of large numbers for the trajectory of quasiparticles in a Toda lattice at thermal equilibrium, demonstrating that they travel with explicit constant velocities through a direct analysis of asymptotic scattering relations and concentration estimates for the system's Lax matrix.

Amol Aggarwal2026-03-31

🔢 mathematics

On the Spectral Geometry and Small Time Mass of Anderson Models on Planar Domains

This paper establishes small-time asymptotics for the Anderson Hamiltonian and parabolic Anderson model on bounded planar domains using probabilistic methods, demonstrating that a single observation of the system's eigenvalues or mass can almost surely recover geometric properties of the domain (such as area, boundary length, or fractal dimension) and the noise variance.

Pierre Yves Gaudreau Lamarre, Yuanyuan Pan2026-03-31

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math-ph

Remarks on "Further comments on "Rebuttal of "Refutation of "Comment on "Reply to "Comments on "A genuinely natural information measure" " " " " " "

The Contextual Modal Logic of a Wigner's Friend Generalization

Separable neighbourhood of identity in C∗^{\ast}∗-algebras

Ground state energy of the Bose--Hubbard model with large coordination number with a polaron-type quantum de Finetti theorem

Fused K-operators and the qqq-Onsager algebra

Evolution of the Torsional Rigidity under Geometric Flows

Differential system related to Krawtchouk polynomials: iterated regularisation and Painlevé equation

Weak Hopf non-invertible symmetry-protected topological spin liquid and lattice realization of (1+1)D symmetry topological field theory

Effective Velocities in the Toda Lattice

On the Spectral Geometry and Small Time Mass of Anderson Models on Planar Domains

Separable neighbourhood of identity in C $^{\ast}$ -algebras

Fused K-operators and the $q$ -Onsager algebra