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

Higher-Rank Orthogonal Twists, APS Boundary Conditions, and $O(2)$ -Equivariant Spectral Flow on a Warped Cylinder

This paper derives an explicit blockwise formula for the $RO(O(2))$ -valued spectral flow of Dirac operators on a finite warped cylinder with higher-rank orthogonal twists and APS boundary conditions, demonstrating how representation-theoretic information is preserved beyond standard integer-valued spectral flow through the decomposition of moving and stationary blocks under reflection symmetry.

Taro Kimura, Sanchita Sharma2026-06-02

🔢 mathematics

A Cohesive $\infty$ -Topos with a Quantum Modality from Finite-Dimensional $C^{*}$ -Algebras

This paper constructs a cohesive $\infty$ -topos equipped with a quantum modality derived from finite-dimensional $C^{*}$ -algebras, providing the first rigorous model for cohesive linear homotopy type theory that interprets decoherence, yields a non-degenerate affine model of multiplicative intuitionistic linear logic, and establishes a synthetic no-cloning theorem.

Joey Woo2026-06-02

🔢 mathematics

Hidden $\mathfrak{u}(2,1)$ symmetry and Jordan chains in a resonant ghostly three-dimensional model

This paper investigates a resonant three-dimensional ghostly Hamiltonian realization of the sixth-order Pais-Uhlenbeck oscillator, revealing a hidden $\mathfrak{u}(2,1)$ symmetry that governs both the classical non-diagonalizable Jordan chain structure and the quantum spectrum, while demonstrating that the associated tri-Hamiltonian formulation lacks a positive-definite generator and yields no independent higher-order integrals.

Andreas Fring, Ian Marquette2026-06-02

🔢 mathematics

Timelike ideal boundary of non-positively curved Lorentzian spaces

This paper introduces the concept of a timelike ideal boundary for non-positively curved Lorentzian length spaces, equips it with a cone topology and angular metric to establish upper curvature bounds, and analyzes its relationship with generalized cones and warping functions.

Saúl Burgos, Mauricio Che, Miguel Prados-Abad2026-06-02

🔢 mathematics

On induced L-infinity action of diffeomorphisms on Cochains

This paper addresses the challenge of defining diffeomorphism actions on cochains within a quantum gravity framework by utilizing homotopy transfer to induce an $L_{\infty}$ action, which is explicitly computed for interval, circle, and square space-times.

Andrey Losev, Dmitrii Sheptunov, Xin Geng2026-06-01

🔢 mathematics

Husain-Kuchař model as the Carrollian limit of the Holst term

This paper demonstrates that the Husain-Kuchař model arises as the Carrollian limit of the Holst term within background-independent field theories and examines the resulting Carrollian symmetry features in its Hamiltonian formulation.

J. Fernando Barbero G., Juan Margalef-Bentabol, Aitor Vicente-Cano, Eduardo J. S. Villaseñor2026-06-01

🔢 mathematics

On dissipation operators of Quantum Optics

This paper investigates dissipation operators within the framework of damped driven Jaynes-Cummings equations for a quantized field coupled to a two-level molecule, establishing the symmetry and non-positivity of the fundamental dissipation operator.

A. I. Komech, E. A. Kopylova2026-06-01

🔢 mathematics

Lecture notes on the flow equation approach to singular stochastic PDEs

This paper presents the flow equation approach as a robust, Wilsonian-inspired framework for solving the renormalization problem across the entire subcritical regime of singular stochastic PDEs by inductively tracking the evolution of nonlinear terms in effective dynamics through a scale-dependent flow equation.

Paweł Duch2026-06-01

🔢 mathematics

BV pushforward as a quasi-isomorphism

This paper proves that the BV pushforward map between a full theory and its effective infrared theory is a quasi-isomorphism by constructing a strong deformation retraction via the homological perturbation lemma, providing two distinct proofs and an explicit path integral formula for the quasi-inverse lifting map.

Alberto S. Cattaneo, Pavel Mnev2026-06-01

🔢 mathematics

Novel energy preserving bijections between affine crystals for $U_q(\widehat{\mathfrak{sl}}_2)$ and integer partitions

This paper constructs an explicit combinatorial bijection between highest weight paths in the crystal graphs of level 1 integrable representations of $U_q(\widehat{\mathfrak{sl}}_2)$ and integer partitions with specific rank statistics, thereby providing a precise combinatorial interpretation of the spinon motif description in Wess-Zumino-Witten conformal field theory.

Sota Miyazawa, Taichiro Takagi2026-06-01

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math-ph

Higher-Rank Orthogonal Twists, APS Boundary Conditions, and O(2)O(2)O(2)-Equivariant Spectral Flow on a Warped Cylinder

A Cohesive ∞\infty∞-Topos with a Quantum Modality from Finite-Dimensional C∗C^{*}C∗-Algebras

Hidden u(2,1)\mathfrak{u}(2,1)u(2,1) symmetry and Jordan chains in a resonant ghostly three-dimensional model

Timelike ideal boundary of non-positively curved Lorentzian spaces

On induced L-infinity action of diffeomorphisms on Cochains

Husain-Kuchař model as the Carrollian limit of the Holst term

On dissipation operators of Quantum Optics

Lecture notes on the flow equation approach to singular stochastic PDEs

BV pushforward as a quasi-isomorphism

Novel energy preserving bijections between affine crystals for Uq(sl^2)U_q(\widehat{\mathfrak{sl}}_2)Uq​(sl2​) and integer partitions

Higher-Rank Orthogonal Twists, APS Boundary Conditions, and $O(2)$ -Equivariant Spectral Flow on a Warped Cylinder

A Cohesive $\infty$ -Topos with a Quantum Modality from Finite-Dimensional $C^{*}$ -Algebras

Hidden $\mathfrak{u}(2,1)$ symmetry and Jordan chains in a resonant ghostly three-dimensional model

Novel energy preserving bijections between affine crystals for $U_q(\widehat{\mathfrak{sl}}_2)$ and integer partitions