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.

On the Optimality of Reduced-Order Models for Band Structure Computations: A Kolmogorov $n$ -Width Perspective

This paper establishes that reduced-order models for phononic, acoustic, and photonic band structure computations achieve exponential convergence rates determined by spectral gaps, as proven via Kolmogorov $n$ -width analysis of holomorphic eigenpairs and spectral projectors, thereby providing a sharp optimality benchmark that validates the effectiveness of greedy algorithms and existing methods like RBME.

Ankit Srivastava2026-04-07🔢 math-ph

From hyperbolic to complex Euler integrals

This paper proves that univariate hyperbolic beta integrals and conical functions degenerate into two-dimensional integrals over the complex plane by establishing uniform bounds on their integrands.

N. M. Belousov, G. A. Sarkissian, V. P. Spiridonov2026-04-07🌀 nlin

From BV-BFV Quantization to Reshetikhin-Turaev Invariants

This paper proposes a program to bridge perturbative BV-BFV quantization of Chern-Simons theory with non-perturbative Reshetikhin-Turaev invariants by conjecturing their equivalence as extended topological quantum field theories, mediated by factorization homology, derived character stacks, and $\mathbb{E}_n$ -Koszul duality.

Nima Moshayedi2026-04-07🔢 math-ph

Optimal, Qubit-Efficient Quantum Vehicle Routing via Colored-Permutations

This paper introduces a qubit-efficient quantum encoding for the capacitated vehicle routing problem using a global-position colored-permutation framework that eliminates the need for explicit load registers, thereby reducing logical qubit overhead while maintaining strong algorithmic performance and recovering verified optima on standard benchmarks.

Chinonso Onah, Kristel Michielsen2026-04-07🔢 math-ph

Uniqueness of gauge covariant renormalisation of stochastic 3D Yang-Mills-Higgs

This paper establishes the uniqueness of the mass renormalisation required to ensure gauge covariance in the local solutions of 3D stochastic Yang-Mills-Higgs equations, utilizing systematic short-time expansions and refined state spaces to strengthen previous results and support the identification of limits for other approximations like lattice dynamics.

Ilya Chevyrev, Hao Shen2026-04-06🔢 math-ph

q-Opers and Bethe Ansatz for Open Spin Chains I

This paper initiates the geometric study of Bethe Ansatz equations for open spin chains by establishing a correspondence between their spectra and a newly defined space of reflection-invariant $q$ -opers, specifically constructing this duality for type-A systems.

Peter Koroteev, Myungbo Shim, Rahul Singh2026-04-06🔢 math-ph

Dimensional consistency in fractional differential equations with non singular kernels

This paper proposes a simple change of variables to resolve dimensional consistency issues when replacing ordinary time derivatives with fractional derivatives in equations featuring non-singular kernels, demonstrating the method's validity through a specific example.

Gabriel Gonzalez2026-04-06🔢 math-ph

Zero-Freeness of the Hard-Core Model with Bounded Connective Constant

This paper establishes that the partition function of the hard-core model is zero-free in a complex neighborhood up to the connective constant threshold $\lambda_c(\mu)$ , thereby proving the uniqueness and analyticity of the free energy density for infinite lattices beyond the traditional maximum degree bounds.

Yuan Chen, Shuai Shao, Ke Shi2026-04-06🔢 math-ph

Classification of Extended Abelian Chern-Simons Theories

This paper establishes that extended Abelian Chern-Simons theories with gauge group $U(1)^n$ are completely classified, up to symmetric monoidal natural isomorphism, by finite quadratic modules, which consequently also classify pointed Abelian Reshetikhin-Turaev TQFTs and pointed modular tensor categories.

Daniel Galviz2026-04-06🔢 math-ph

Worldsheet Duals to One-Matrix Models

This paper establishes a concrete closed string dual for any interacting Hermitian one-matrix model in the standard 't Hooft regime by identifying the worldsheet theory as a supersymmetric B-twisted Landau-Ginzburg model coupled to 2d topological gravity, thereby providing a precise dictionary that matches matrix and string correlators to all orders in the genus expansion and 't Hooft coupling.

Alessandro Giacchetto, Rajesh Gopakumar, Edward A. Mazenc2026-04-06⚛️ hep-th

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math-ph

On the Optimality of Reduced-Order Models for Band Structure Computations: A Kolmogorov nnn-Width Perspective