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.
This paper formulates and solves -equivariant Seiberg-Witten equations on irreducible Hermitian symmetric spaces by employing a canonical twisted Hodge operator, revealing that the resulting moduli spaces are characterized by representation-theoretic Weyl group data and collapse to single gauge classes in the compact case or lie outside the discrete series in the non-compact case.
This paper establishes a sharp, explicit algebraic lower bound for the first Dirichlet eigenvalue on compact Riemannian manifolds with positive Ricci curvature and nonnegative boundary mean curvature, which is derived from the first two moments of a model potential, proven to be the geometric infimum, and strictly improves upon previous variance-based estimates.
This paper establishes that exact permutation covariance precludes sparse metric geometry and derives quantitative no-go theorems for relational Hamiltonians, while constructing two exactly solvable finite models that demonstrate specific trade-offs between clock resources, locality, and spectral gaps without yielding an emergent geometric phase.
This paper critiques the Landau-level model proposed by Sierra and Townsend for the Riemann zeros by demonstrating that higher Landau levels do not generate the necessary term due to energy-independent boundary phase shifts, and by identifying the origin of the term in their semiclassical equation as a first-order shift of the smooth counting function.
This paper leverages Howe duality to establish an exact SU() symmetry resolution for Bose-Hubbard models that reveals universal spectral properties and a precise boson-fermion partition function identity, enabling the analysis of diverse phenomena ranging from color ferromagnetism in unfrustrated systems to singlet-cluster states in frustrated lattices.
This paper introduces a spinorial framework for -differential forms on Minkowski spacetime by establishing the correspondence between spacetime and Hermitian matrices, constructing spinor-based differential forms and the Dirac operator, and extending the formalism to non-monogenic functions to demonstrate its utility in relativistic field equations and quantum geometry.
This paper solves the inverse resonance problem for the one-dimensional Schrödinger operator on the half-line with a compactly supported complex potential and a complex Robin boundary condition by adapting the transformation-operator and entire-function methods of Marletta, Shterenberg, and Weikard to establish uniqueness, stability, and large-energy estimates for the Robin characteristic function.
This paper determines the best constants for estimates of functions on spheres with bounded Laplacian and vanishing first spherical harmonic components, expressing them through weighted extremal polynomials and revealing that these constants are strictly smaller than the corresponding Bohr–Favard constants.
This paper provides a direct tensor-categorical proof that lifting symmetries from a slightly degenerate braided fusion category to a fixed minimal nondegenerate extension yields exactly two distinct locality-respecting classes related by fermion attachment, characterized by a surjective restriction homomorphism with a central kernel.
This paper disproves the Rényi area-law conjecture for all in dimensions two and higher by constructing gapped, finite-range Hamiltonians whose unique ground states obey a von Neumann area law while exhibiting volume-law Rényi entanglement due to error-space complexity.