1694 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 the $so(N+1,2)$ dynamical symmetry of the quantum Calogero-Coulomb model using Dunkl operators, classifying its wave functions into infinite-dimensional lowest-weight $so(1,2)$ multiplets and expressing the Hamiltonian's linear spectrum via the conformal subalgebra.
This paper establishes the theoretical foundations for the linear and direct sampling methods to qualitatively recover supported cavities in thin elastic plates governed by the biharmonic wave equation, demonstrating through numerical experiments that both methods robustly identify obstacle locations, with the direct sampling method offering superior stability and computational efficiency.
This paper introduces a linear-algebraic framework that utilizes logarithmic variables to systematically determine independent dimensionless quantities and eliminate redundancies in dimensional analysis, particularly for complex systems with numerous variables or implicit constraints where traditional elimination methods are impractical.
This paper derives exact bound-state solutions and energy spectra for a spin-1/2 fermion governed by the Dirac equation with a general combination of scalar, vector, and tensor Coulomb potentials in 3+1 dimensions, establishing a direct mapping between planar and spherical problems while validating existing results and introducing new cases involving broken spin and pseudospin symmetries.
This paper presents a novel classification of unitarizable supermodules over the special linear Lie superalgebra by utilizing an algebraic quadratic Dirac operator and a corresponding Dirac inequality.
This paper demonstrates that non-Hermiticity in a two-qubit asymmetric Heisenberg $XY$ system can induce a thermal entanglement phase transition, where maximal entanglement emerges above a critical non-Hermiticity threshold due to ground state degeneracy rather than exceptional points, while proposing a singular-value-decomposition approach for computing entanglement in such bi-orthogonal systems.
This paper proposes a robust, automated method combining Fourier analysis and statistical classification to reliably identify and distinguish chimera states from other dynamical patterns in complex coupled oscillator systems, demonstrating its effectiveness and generalizability across varying network topologies and parameters.
This paper provides an accessible review of symplectic fermions, a logarithmic conformal field theory with central charge $-2$, by explicitly constructing its field space and correlation functions while discussing its logarithmic structure within the context of lattice model scaling limits.
This paper introduces the magnetic Euler-Arnold equation by combining Arnold's geometric approach to fluid dynamics with his formulation of charged particle motion in magnetic fields, demonstrating that several important infinite-dimensional systems—including the Korteweg-de Vries and global quasi-geostrophic equations—can be interpreted as such magnetic geodesic flows while establishing new well-posedness results.
This paper demonstrates that the standard QAOA faces intrinsic feasibility bottlenecks on constrained problems with low-dimensional solution manifolds, but introduces a constraint-embedded variant (CE QAOA) that achieves provable exponential enhancement in feasible solution probability by operating directly within the valid subspace.