1605 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 establishes a generalized crystalline equivalence principle that proves an equivalence between topological quantum field theories (TQFTs) with spatial -symmetry and those with internal symmetry, while simultaneously providing a unified framework for defining and classifying anomalies in both spatial and categorical symmetry contexts.
This paper utilizes Random Matrix Theory to investigate spectral fluctuations in multilayer networks, demonstrating that universal statistical features persist across varying connectivity configurations and successfully modeling the crossover between independent and fully coupled layer statistics, with applications validated on real protein structures.
This paper proves that weakly interacting spinful lattice fermions coupled to a dynamical gauge field in the -flux phase form a topologically ordered, fully gapped system where dressed monopole excitations exhibit toric code braiding statistics with fermions and vanish self-braiding due to zero Hall conductance.
This paper presents a mathematical framework extending symmetry reduction to classical field theories within the De Donder-Weyl multisymplectic formalism, allowing for the identification and removal of redundant, empirically inaccessible global scale degrees of freedom while preserving Lorentz covariance.
This paper introduces "folded optimal transport," a unified framework that extends cost functions from extreme boundaries to entire convex sets using Choquet theory, thereby generalizing classical optimal transport and enabling the construction of a separable quantum Wasserstein distance on density matrices derived from pure states.
This paper demonstrates that the Gel'fand-Yaglom theorem and the Green's function method are completely equivalent for computing ratios of functional determinants of one-dimensional operators through a contour integral argument, while also providing a natural prescription for handling vanishing and negative eigenvalues.
This paper characterizes equilibrium measures for higher-dimensional rotationally symmetric Riesz gases by establishing a converse construction that links prescribed power-series densities to their associated external potentials, utilizing hypergeometric identities to derive explicit solutions for various confining fields and applying the framework to Coulomb gases in half-spaces.
This paper establishes a rigorous framework for non-ergodic quantum dynamics by demonstrating how local causal constraints, modeled via "wall" unitaries, arrest operator spreading and induce entanglement area laws through the invariance of embedded operator algebras and connections to quantum error-correcting codes.
This paper investigates the impact of soft versus hard boundary enforcement techniques on the accuracy and training efficiency of physics-informed neural networks (PINNs) for elastodynamic problems, demonstrating that while hard enforcement of traction conditions on implicit geometries reduces runtime, it often trades off against solution accuracy compared to soft enforcement.
This paper develops a spectral theory for scale-invariant operators on the multiplicative half-line using Mellin transforms to demonstrate that geometric and spectral exponents are fundamentally decoupled, providing a precise mathematical characterization of multicriticality where their inequality signals multiple independent scaling dimensions.