2548 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 constructs a decorated Spin-TQFT framework based on a novel quantization of Chern-Simons theory to compute invariants, thereby deriving comprehensive surgery formulas, explicit expressions for various manifolds, and generalizations to higher-rank gauge groups.
This paper introduces the Stäckel lift as a unified geometric framework that extends classical Eisenhart lifts to construct new classes of integrable Hamiltonian systems endowed with non-trivial symplectic-Haantjes structures, with specific applications to magnetic systems and modified gravity theories.
This paper proposes a branchwise formulation of metric gravity where the spacetime signature is encoded by an internal field, demonstrating that among various possible signature vacua, only the standard Lorentzian branch satisfies the necessary conditions for causal viability, thereby offering an anthropic explanation for the observed signature of our universe.
This paper demonstrates that in three-dimensional liquid drop models with screened Riesz-type interactions (specifically truncated Coulomb and Yukawa potentials), the classical result that balls are the unique minimizers fails, as the authors prove the existence of connected, non-radial minimizers through a comparative energy analysis of balls, core-shells, and cylinders.
This paper investigates the complex Ginibre ensemble conditioned on an overcrowding event where a fraction of eigenvalues are forced outside a disk, deriving asymptotic probability estimates and characterizing the resulting non-determinantal conditional distribution as converging to a standard Ginibre ensemble in the bulk and a hard-wall determinantal process near the boundary.
This paper establishes Rule 22 as a symmetric, algebraically tractable reference for elementary cellular automata by deriving exact closed-form solutions for its single-seed orbit and using it to characterize the symmetry-breaking deviations and apparent randomness of Rule 30.
This paper introduces Symplectic Geometric Closure (SGC), a stochastic field theory that preserves the Hamiltonian geometry of fluid dynamics by coupling resolved vorticity to a hidden reservoir, thereby achieving accurate turbulence closure, eliminating spurious sweeping decorrelation, and naturally reproducing Kraichnan's dual cascades through endogenous, memory-controlled transport.
This paper demonstrates that in Whitney-discretized electromagnetism, the relative entropy of Gaussian distributions under gauge reduction decomposes into the relative entropy of physical marginals plus a nonnegative conditional gauge contribution, providing an information-geometric framework where the physical divergence is identified as the minimum over all auxiliary extensions.
This paper presents a systematic framework using a many-body spectral localizer to identify topological pre-thermal scars in interacting quantum systems and explicitly construct approximate quantum error-correcting codes from them, thereby establishing a general route to protect quantum information without prior knowledge of microscopic scarring mechanisms.
This paper establishes an exact correspondence between fat-point interpolation in complex projective space and a dark-state problem for fixed-particle-number bosons, leveraging this quantum reformulation and arithmetic amplification techniques to prove Demailly's conjectured inequality regarding the Waldschmidt constant.