2253 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.
The paper proves the existence and uniqueness of a mathematical model for in situ leaching by using homogenization to derive a macroscopic description and applying Banach's fixed-point theorem to resolve the nonlinear free-boundary problem between the solid and liquid components.
This paper refines the postulate that charge quantization is governed by a homotopy type , demonstrating that while its homotopy groups classify brane charges, its homology groups classify invertible higher-form symmetries, and ultimately shows that the requirement for to be contractible in quantum gravity imposes Swampland-like constraints, such as ruling out noncompact gauge groups.
This paper explores the mathematical connection between the Hahn-Banach Theorem and the Second Law of Thermodynamics, demonstrating how the theorem guarantees the existence of entropy and temperature functions for any material state while establishing that their uniqueness depends on the reachability of states via reversible processes.
This paper proposes a new geometric framework for multiple zeta values based on "non-linear" determinantal integral representations, connecting them to diverse fields such as tropical geometry, Feynman integrals, and the reduction theory of quadratic forms.
This paper uses an algebraic approach to study free Carrollian quantum field theories, demonstrating that while massive theories allow for regular vacuum and thermal states, massless theories exhibit more complex behaviors that necessitate a Hilbert space representation consisting of both a standard Fock sector and a nonseparable zero-mode sector, providing new insights into the role of infrared degrees of freedom in flat space holography.
This paper establishes a combinatorial theory of discrete vector bundles with connection on locally ordered simplicial complexes, introducing a discrete exterior covariant derivative that mirrors smooth geometric structures and satisfies key identities like the Bianchi identity, while also linking flat connections to twisted de Rham cohomology and providing a concrete comparison with existing frameworks.
This paper presents a microscopic derivation of a -symmetric non-Hermitian sine-Gordon effective theory from a nonequilibrium spin-boson system using Keldysh functional integrals, establishing a precise dictionary between microscopic parameters and effective couplings to demonstrate that the resulting renormalization group flow, exceptional point physics, and bound-state spectrum align with established non-Hermitian sine-Gordon results.
This paper derives an effective model on a non-simply connected domain from the Ginzburg–Landau theory in a planar simply connected domain under a strong, compactly supported magnetic field, revealing oscillatory phenomena characteristic of the Little-Parks and Aharonov–Bohm effects.
This paper develops a discrete Euler-Poincaré reduction framework for mechanical systems with advected parameters and additional dynamics using group difference maps, extends the Kelvin-Noether theorem to this discrete setting, and demonstrates the method's effectiveness in preserving geometric properties through applications to underwater vehicle dynamics and numerical simulations.
This paper constructs self-catalytic branching Brownian motions with an infinite number of initial particles for the subcritical case and establishes their coming down from infinity property along with characterizing the associated convergence rates.