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 establishes a theoretical framework linking the symmetry-enforced zeros of electronic wavefunctions at high-symmetry momenta to band topology, enabling the direct experimental determination of topological invariants via scanning tunnelling microscopy and providing insights into interaction effects in correlated materials.
This paper demonstrates how the traveling-wave solution of the nonlinear Schrödinger equation maps onto the curvature equation of a closed 3D elastica knot, revealing that the constraint of spatial periodicity necessitates an extension of the classical elastica-knot parameter space to accommodate specific knot parameters derived from the wave's velocity and circulation.
This paper introduces and derives the unit Killing initial data (uKID) equations, a system of differential equations on an initial data surface that uniquely characterizes unit-normalized Killing vector fields in Einstein -vacuum spacetimes by eliminating the scaling degree of freedom found in classical KID equations.
This paper classifies all six-dimensional real nilpotent Lie bialgebras of symplectic type, derives the Poisson structures on their associated Poisson-Lie groups, and identifies new integrable Hamiltonian systems utilizing these groups as phase spaces and their duals as symmetry groups.
This paper introduces the concept of rough additive functions to establish a PDE-based framework for defining controlled gauge transformations and holonomies, proving a rough version of Uhlenbeck compactness via regularity structures, and demonstrating an optimal regularity gauge-fixed representation of the 2D Yang-Mills measure on the unit square.
This paper establishes model-independent potential-theoretic criteria for the collision and non-collision of reversible infinitely many interacting diffusion processes on the real line, relying on correlation functions and conditional densities rather than specific interaction structures, and applies these results to prove that the collision set for the -symmetric Dirichlet form is polar if and only if .
This paper compares numerical stabilization methods for transport-dominated atmospheric flows using Julia and Python implementations, finding that while quasi-monotone limiters best minimize unphysical extrema, the SUPG method excels at preserving sharp features despite not improving error metrics over the unstabilized case.
This paper demonstrates that the alternating continuous and projective evolution of quantum dynamics can be unified into a single differential equation on a refined state space manifold, thereby enabling the application of standard port-theoretic analysis and control techniques.
The authors demonstrate that the self-correcting memory in 3d Wegner gauge theory remains stable against arbitrary small perturbations through a novel "gauge averaging" method, which reveals that the phase is fluctuation-stabilized with robustness that increases with temperature up to a critical point.
This paper constructs the sine-Gordon measure and its renormalized effective potential in finite volume up to the seventh threshold by employing a weak stochastic control problem, an associated weak FBSDE, and a multipole Mayer expansion within a fully inductive framework that covers the entire subcritical regime.