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.

🔬 physics

Comparison of Structure-Preserving Methods for the Cahn-Hilliard-Navier-Stokes Equations

This paper introduces and validates two new structure-preserving discontinuous Galerkin methods, SWIPD-L and SIPGD-L, for the Cahn-Hilliard-Navier-Stokes equations with degenerate mobility, demonstrating that they achieve optimal convergence, preserve key physical properties like mass conservation and energy dissipation, and offer significant computational savings on adaptive meshes compared to existing approaches.

Jimmy Kornelije Gunnarsson, Robert Klöfkorn2026-03-06

⚛️ quantum physics

Tight inapproximability of max-LINSAT and implications for decoded quantum interferometry

This paper proves that max-LINSAT is tightly inapproximable within any constant factor beyond the random-assignment ratio $r/q$ under $\mathsf{P} \neq \mathsf{NP}$ , a hardness threshold that coincides with the asymptotic performance limit of decoded quantum interferometry, thereby delineating the boundary between classical worst-case hardness and potential quantum advantage.

Maximilian J. Kramer, Carsten Schubert, Jens Eisert2026-03-06

🔬 physics

Split Casimir Operator of the Lie Algebra so(2r) in Spinor Representations, Colour Factors and Yang-Baxter Equation

This paper derives characteristic identities for the split Casimir operator of the Lie algebra $so(2r)$ in spinor representations to construct invariant projectors, calculate colour factors for ladder Feynman diagrams in $Spin(2r)$ gauge theories, and obtain a new $so(2r)$-invariant solution to the Yang-Baxter equation.

A. P. Isaev, A. A. Provorov2026-03-06

🔬 physics

Drinfeld Correspondence in Infinite Dimensions

This paper establishes the Drinfeld correspondence between Poisson Lie groups and Lie bialgebras in the infinite-dimensional setting, specifically extending the theory to regular Lie groups modeled on convenient vector spaces such as nuclear Fréchet and Silva spaces, with applications to loop groups and diffeomorphism groups.

Praful Rahangdale2026-03-06

🔬 physics

Causal Fermion Systems, Non-Commutative Geometry and Generalized Trace Dynamics

This paper compares causal fermion systems, non-commutative geometry, and generalized trace dynamics, highlighting their shared recovery of fiber bundle structures in the continuum limit and identifying the encoding of spacetime relations via a generalized two-point correlator—replacing Synge's world function—as the key innovation that can be unified across all three frameworks.

Felix Finster, Shane Farnsworth, Claudio F. Paganini, Tejinder P. Singh2026-03-06

🔬 physics

Dyson Brownian motion on a Jordan curve

This paper provides a rigorous construction of Dyson Brownian motion on a rectifiable Jordan curve and analyzes its fundamental properties, including the associated Fokker-Planck-Kolmogorov equation, convergence to the stationary Coulomb gas distribution, low-temperature large deviations, and the limiting McKean-Vlasov equation in the many-particle regime.

Vladislav Guskov, Mingchang Liu, Fredrik Viklund2026-03-06

🔬 physics

Well-posedness of the heat equation in domains with topological transitions

This paper establishes the well-posedness of the heat equation with homogeneous Dirichlet boundary conditions in time-evolving domains undergoing topological transitions by introducing anisotropic space-time function spaces and applying the Babuška-Banach theorem to prove existence, uniqueness, and a priori estimates for weak solutions.

Maxim Olshanskii, Arnold Reusken2026-03-06

🔬 physics

The Gibbs phenomenon for the Krawtchouk polynomials

This paper investigates the Gibbs phenomenon in the Fourier approximation of the sign function using Krawtchouk polynomials, demonstrating that unlike classical orthogonal polynomials, it exhibits a distinct Gibbs constant and a bounded steepness that converges to $\log 4$ as the degree increases.

John Cullinan, Elisabeth Young2026-03-06

🔬 physics

Birkhoffs Theorem and Lie Symmetry Analysis

This paper employs Lie Symmetry Analysis and Noether Point Symmetry methods to derive the symmetry generators and conserved quantities of the Einstein vacuum field equations, thereby offering a novel reformulation of Birkhoff's Theorem.

Avijit Mukherjee, Subham B Roy2026-03-05

🔬 physics

Six-dimensional supermultiplets from bundles on projective spaces

This paper utilizes the isomorphism between the six-dimensional nilpotence variety and $\mathbb{P}^1 \times \mathbb{P}^3$ within the pure spinor superfield formalism to classify and explicitly construct various six-dimensional supermultiplets, including vector, hyper, and supergravity multiplets, by associating them with line bundles and higher-rank equivariant vector bundles on projective spaces.

Fabian Hahner, Simone Noja, Ingmar Saberi, Johannes Walcher2026-03-05

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