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.

A Lagrangian framework for canonical analysis for the Holst model with $\beta = 0$

This paper presents a canonical analysis of the Holst model for General Relativity with the Barbero parameter set to $\beta=0$ and unconstrained lapse and shift functions, deriving a complete system of 37 equations that confirms consistency with standard Einstein dynamics while revealing new differential constraints dependent on gauge choices, thereby establishing a viable foundation for extending Loop Quantum Gravity to dimensions beyond $3+1$ .

Roberto Ciccarelli, Lorenzo Fatibene2026-04-22⚛️ gr-qc

Orlov-Schulman symmetries of the self-dual conformal structure equations

This paper constructs and proves the compatibility of Orlov-Schulman symmetries for the self-dual conformal structure hierarchy, illustrating their properties through examples like Galilean transformations and scalings while presenting a dressing scheme formulation based on the Riemann-Hilbert problem.

L. V. Bogdanov2026-04-22🌀 nlin

The Cohomology of Solvmanifold SYZ Mirrors

This paper investigates non-Kähler SYZ mirror symmetry for solvmanifolds by establishing the correspondence between supersymmetric cycles via Fourier-Mukai transforms, deriving Lie-theoretic criteria to construct and classify explicit mirror pairs from almost abelian and nilpotent Lie groups, and elucidating the role of Tseng-Yau cohomology through its connection to noncommutative geometry.

Leonardo F. Cavenaghi, Lino Grama, Ludmil Katzarkov, Pedro Antonio Muniz Martins2026-04-22⚛️ hep-th

Painlevé Asymptotics of the Focusing Nonlinear Schrödinger Equation with a Finite-Genus Algebro-Geometric Background

This paper employs the Riemann–Hilbert approach and the Deift–Zhou nonlinear steepest descent method to analyze the long-time asymptotics of the focusing nonlinear Schrödinger equation with finite-genus algebro-geometric initial data, revealing that odd-genus backgrounds yield leading-order behavior described by the second Painlevé transcendent while even-genus backgrounds are characterized by parabolic cylinder functions.

Ruihong ma, Engui Fan2026-04-22🔢 math-ph

The Minimal Attached Eddy in Wall Turbulence: Statistical Foundations, Inverse Identification and Influence Kernels

This paper advances Townsend's attached eddy hypothesis by formulating an inverse problem to derive influence kernels from DNS data, which are then used to construct and validate a minimal, Biot-Savart-consistent hairpin eddy model that successfully reproduces mean velocity and Reynolds stress statistics across high Reynolds numbers through a novel scale-by-scale decomposition.

Karthik Duraisamy2026-04-21🔢 math-ph

The difference variational bicomplex and multisymplectic systems

This paper constructs the difference variational bicomplex to provide a coordinate-free framework for analyzing finite difference variational problems, establishes the link between Hamiltonian existence and multisymplecticity in partial difference equations, defines difference multimomentum maps for conservation laws, and extends these results to multisymplectic integrators on non-uniform meshes through local scaling.

Linyu Peng, Peter E. Hydon2026-04-21🔢 math-ph

Sturm-Liouville operators with periodically modulated parameters. Part I: Regular case

This paper introduces a new class of Sturm-Liouville operators with periodically modulated parameters and proves that, under specific assumptions regarding their monodromy matrix at zero, their spectral density is a continuous and positive function everywhere on the real line.

Grzegorz Świderski, Bartosz Trojan2026-04-21🔢 math-ph

A Kac system interacting with two heat reservoirs

This paper demonstrates that a system of $M$ particles in three dimensions interacting with two finite heat reservoirs via Kac-type collisions behaves effectively as if coupled to infinite thermostats for times significantly shorter than $\sqrt{N}$ , while also extending existing results to the three-dimensional case when the reservoir temperatures are equal.

Federico Bonetto, Michael Loss, Matthew Powell2026-04-21🔢 math-ph

Planar percolation and the loop O(n) model

This paper proves that a broad class of planar site percolation processes satisfying tail triviality, positive association, and stochastic domination exhibits either zero or infinitely many infinite components, thereby resolving a 1996 conjecture by Benjamini and Schramm and confirming a key aspect of Nienhuis's 1982 phase diagram for the loop O(n) model on the hexagonal lattice.

Alexander Glazman, Matan Harel, Nathan Zelesko2026-04-21🔢 math-ph

From gauging to duality in one-dimensional quantum lattice models

This paper demonstrates that gauging and duality transformations in one-dimensional quantum lattice models are equivalent up to constant depth quantum circuits by utilizing matrix product operators to represent global symmetries and classify duality transformations, thereby clarifying the handling of static background fields in generalized symmetry gauging.

Bram Vancraeynest-De Cuiper, José Garre-Rubio, Frank Verstraete, Kevin Vervoort, Dominic J. Williamson, Laurens Lootens2026-04-21🔢 math-ph

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math-ph

A Lagrangian framework for canonical analysis for the Holst model with β=0\beta = 0β=0