🔢 Category

math-ph

3210 papers

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.

⚛️ general relativity

Structure of the Riemann tensor in higher-dimensional Kerr-NUT-(A)dS spaces

This paper investigates the algebraic and differential structure of the Riemann tensor in higher-dimensional Kerr-NUT-(A)dS spaces to pursue an IDEAL characterization of these metrics, proving a no-go theorem that no non-trivial 2-form can be covariantly constructed from the undifferentiated Riemann tensor alone while successfully characterizing the family of valid curvature tensors through specific algebraic and differential conditions derived from the principal tensor's integrability and the Bianchi identity.

Igor Khavkine, David Matejov2026-09-01
🔢 mathematics

Endpoint Mapping Properties of Wave Operators for Two-Dimensional Schrödinger Operators

This paper establishes the complete LpL^p mapping properties of two-dimensional Schrödinger wave operators at the critical endpoints p=1p=1 and p=∞p=\infty, revealing that unlike in higher dimensions, an s-wave resonance at zero energy unexpectedly improves endpoint boundedness while other spectral configurations impose specific Calderón–Zygmund type estimates or require precise moment cancellations for boundedness.

Han Cheng, Changxing Miao, Xiaohua Yao2026-09-01
🔢 mathematics

On the discrete spectrum of Dirac operators with Lorentz-scalar δ\delta-shell interactions supported on unbounded curves

This paper establishes that a massive Dirac operator in the plane with an attractive Lorentz-scalar δ\delta-shell interaction supported on a smooth, unbounded curve that locally deforms a broken line possesses a finite number of discrete eigenvalues within its spectral gap, provided the curve bounds a convex domain and the interaction strength is sufficiently extreme, thereby demonstrating that the discrete spectrum is induced by the geometric deformation of the support.

Markus Holzmann, Vladimir Lotoreichik, Marco Vogel2026-09-01
🔢 mathematics

On the equivalence between the Polchinski flow and the Connes-Kreimer approaches to perturbative renormalisation

This paper establishes the equivalence between the Polchinski flow and Connes-Kreimer approaches to perturbative renormalisation by demonstrating that a combinatorial procedure based on decorated graphs solves the Polchinski equation, thereby deriving a highly general form of the renormalised potential for Euclidean quantum field theories.

Yvain Bruned, Paul Laubie, Aurélien Minguella2026-09-01
🔢 mathematics

Boundary Quantum Knizhnik-Zamolodchikov Equations and Integrability of Quantum Field Theories with Time-Dependent Bulk and Boundary Coupling Strengths

This paper extends a generalized Bethe ansatz framework to open boundary conditions with time-dependent bulk and boundary couplings, demonstrating that integrability leads to boundary quantum Knizhnik-Zamolodchikov (BqKZ) equations whose solutions yield exact wavefunctions and reveal that the dynamical invariants of the time-dependent model correspond to the renormalization group invariants of the associated static system.

Parameshwar R. Pasnoori2026-09-01
🔢 mathematics

Bosonic codes from compact phase spaces

This paper establishes the algebraic structure of bosonic quantum error-correcting codes on genus-two Riemann surfaces by constructing code words as automorphic forms, while proving a fundamental no-go theorem that non-amenable stabilizer groups on higher-genus surfaces preclude the existence of normalizable exact code states, thereby distinguishing them from standard GKP codes.

David Roberts, Aaron Slipper, Alireza Parhizkar, Victor V. Albert, Mohammad Hafezi2026-09-01