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.

Spectral separation of variables from equivalent Lagrangian systems

This paper demonstrates that requiring two quadratic Lagrangians to generate identical Euler-Lagrange equations imposes a commutation condition between their kinetic matrices and the potential's Hessian, which enables an orthogonal spectral decomposition of the configuration space to decouple the equations of motion into independent subsystems, thereby recovering classical integrable regimes in systems like Sawada-Kotera and Hénon-Heiles.

Mattia Scomparin2026-05-18🔢 math-ph

Nonlocal Optical Response and Surface Susceptibilities: A Systematic Derivation via Spatial Moment Expansion

This paper presents a systematic theory that derives effective surface susceptibilities for arbitrary curved interfaces by applying a spatial moment expansion to nonlocal optical response kernels, thereby generalizing Feibelman's $d$ -parameters to include curvature corrections and establishing generalized Maxwell boundary conditions.

Frédéric Zolla2026-05-18🔬 physics.optics

Turbulent stretching of FENE dumbbell polymer model via special stochastic scaling and singular limits

This paper establishes a pathwise deterministic limit for the FENE polymer density equation in random turbulent flow, revealing a new second-order operator that captures average turbulent stretching, and subsequently identifies the stationary distribution of polymer length as the time-scale vanishes.

Federico Butori, Yassine Tahraoui2026-05-18🔢 math-ph

Multicritical Scaling Limit of Shifted Schur Measure

This paper investigates the multicritical scaling limit of shifted Schur measures, explicitly determining the limit shape of strict partitions and demonstrating that the edge scaling limit of the correlation function converges to a higher-order Airy kernel determinant, thereby rigorously establishing a transition from a Pfaffian point process to a determinantal distribution.

Haruna Aida, Taro Kimura2026-05-18🔢 math-ph

Quantum game theory for 2 2 games: a mathematical framework

This paper establishes a rigorous mathematical framework for quantum 2x2 games using the Eisert-Wilkens-Lewenstein protocol, extending classical concepts to arbitrary unitary and mixed strategies while proving the existence of Nash equilibria in the quantum setting.

Gloria Ferraris, Veronica Umanità2026-05-18🔢 math-ph

Physics on manifolds with exotic differential structures

This paper demonstrates that identical topological manifolds, specifically the 7-sphere endowed with inequivalent differential structures, can support distinct physical laws, as evidenced by explicit variations in the Dirac operator spectrum under a Kaluza-Klein reduction to SO(4) Yang-Mills gauge theory.

Ulrich Chiapi-Ngamako, M. B. Paranjape2026-05-15🔢 math-ph

Gravitational collapse of matter fields in de Sitter spacetimes

This paper investigates the spherically symmetric gravitational collapse of diverse matter fields in de Sitter spacetime by combining analytical and numerical methods to demonstrate that the quasilocal formalism of marginally trapped surfaces effectively tracks the evolution of black hole and cosmological horizons.

Akriti Garg, Ayan Chatterjee2026-05-15🔢 math-ph

Quantum Wasserstein distance and its relation to several types of fidelities

This paper establishes connections between various definitions of quantum Wasserstein distance and quantum fidelities by proving that optimizing over separable bipartite states yields quantities equal to the Uhlmann-Jozsa fidelity (specifically for qubits) and the superfidelity, while also demonstrating the triangle inequality for certain cases involving pure states.

Géza Tóth, József Pitrik2026-05-15🔢 math-ph

Fermionic Love number of Reissner-Nordström black holes

This paper demonstrates that, unlike their bosonic counterparts which vanish, static fermionic tidal Love numbers are non-zero for non-extremal Reissner-Nordström black holes, highlighting a universal distinction in how black holes respond to fermionic versus bosonic tidal perturbations.

Xiankai Pang, Yu Tian, Hongbao Zhang, Qingquan Jiang2026-05-15🔢 math-ph

Non-local Dirichlet forms, Gibbs measures, and a cohomological Dirichlet principle for Cantor sets

This paper investigates the spectral properties of generators for non-local Dirichlet forms on ultrametric path spaces of Bratteli diagrams and establishes a cohomological Dirichlet principle guaranteeing unique energy-minimizing representatives for cohomology classes when the parameter $\gamma$ exceeds a sharp bound determined by the diagram's structure and the measure-theoretic entropy of the associated Gibbs measure.

Rodrigo Treviño2026-05-15🔢 math-ph

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