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.

⚛️ high-energy theory

Excitability of Gaussian states with VEVs

This paper extends the criteria for exciting one Gaussian state from another in generalized free field theories to include states with nonzero vacuum expectation values, proving that excitability requires both specific conditions on connected two-point functions and a bounded difference in VEVs, and demonstrating that in anti-de Sitter spacetime, a VEV shift is excitable if and only if its boundary extrapolation is excitable in the dual conformal field theory.

Jacqueline Caminiti, Federico Capeccia, Jonathan Sorce2026-06-24

🌀 nonlinear sciences

The KdV vacuum operator and its Katz extension

This paper defines a connection on the formal disc that identifies the vacuum of the Drinfeld-Sokolov KdV hierarchy, extends it canonically to the sphere via Katz extension expressed through Kac coordinates, and demonstrates that this extension represents an additional symmetry within the integrable hierarchy.

Martin T. Luu2026-06-24

🔢 mathematics

Weyl orbit particles

This paper generalizes the known relationship between affine Toda theory mass spectra and Cartan matrix eigenvectors to variants defined by arbitrary Weyl group elements, demonstrating how particle masses correspond to root orbits and applying this framework to calculate the spectrum for the non-Coxeter infinite family $\textrm{D}_{2n}(a_{n-1})$ .

Martin T. Luu2026-06-24

🔢 mathematics

Forms, half-densities, and the quantum odd symplectic category in the BV formalism

This paper provides a detailed review of the geometric foundations of the Batalin-Vilkovisky formalism, specifically focusing on forms and half-densities, and explains their integration into the quantum odd symplectic category via the odd quantization functor.

Pavol Ševera2026-06-24

🔢 mathematics

Gradient Mean-Field Dynamics with Measure-Valued States: Well-Posedness, Chaos, and Long-Time Stability

This paper establishes the well-posedness, propagation of chaos, and long-time exponential stability of a stochastic mean-field interacting particle system defined on a state space combining spatial variables and probability measures, driven by Brownian diffusion and projected cylindrical noise.

Anderson Melchor Hernandez2026-06-24

🔢 mathematics

Morse momentum wavefunctions and rational functions

This paper demonstrates that the momentum-space bound states of the Morse potential are finite rational functions that belong to the framework of rational bispectrality and $R_{II}$ -type systems, specifically identifying them as symmetric biorthogonal rational functions and expressing them via Meixner–Pollaczek polynomials to provide a concrete quantum-mechanical realization of these mathematical structures.

Luc Vinet, Alexei Zhedanov2026-06-24

🔢 mathematics

Zeta-regularization and natural boundaries: Sums and products of integers and primes

This paper extends zeta-regularization techniques beyond natural boundaries to derive the regularized sum of all primes and establish general relationships between the regularized products of integers and primes across nine imaginary quadratic fields.

P. L. Krapivsky, J. M. Luck2026-06-24

🔢 mathematics

The Vector and Canonical Components of the Momentum Operator in 3D Euclidean Space Spanned by General Curvilinear Coordinates

This paper presents a unified approach to constructing the Hermitian vector and canonical components of the momentum operator in 3D Euclidean space with general curvilinear coordinates by defining momentum as mass times velocity via the Heisenberg equation of motion, a method first illustrated with polar coordinates before being generalized.

M. S. Shikakhwa2026-06-24

🔢 mathematics

Toeplitz Determinants and Admissible Correlation Intervals

This paper utilizes the Desnanot–Jacobi determinant identity to derive a simple determinantal representation for the widths of admissible correlation intervals in homogeneous one-dimensional random fields, thereby recovering and contextualizing previous results by Schneider and Hartlap within the framework of classical Toeplitz determinant theory.

Thomas Erben2026-06-24

🔢 mathematics

The sine Gordon equation in light-cone coordinates on the half lines revisited: a Riemann--Hilbert approach

This paper employs a Riemann–Hilbert approach to demonstrate that the initial boundary value problem for the sine-Gordon equation on the right half-line is uniquely determined by initial data alone, whereas the problem on the left half-line requires additional boundary data to be well-posed.

Iryna Karpenko2026-06-24

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