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 introduces a layer potential representation for solving the scattering problem in open wave-guide networks by constructing fundamental solutions via Fourier transform, reducing the transmission problem to solvable Fredholm integral equations of the second kind, and analyzing the resulting guided modes.
This paper establishes that solutions to the integral equations derived from an open wave-guide scattering model possess asymptotic expansions, which are then used to prove that the corresponding partial differential equation solutions satisfy the necessary outgoing radiation conditions.
This paper establishes the local existence of mass-conserving solutions for an inhomogeneous coagulation equation with a sedimentation transport term, demonstrating that spatial inhomogeneity prevents instantaneous gelation or non-existence phenomena observed in the corresponding spatially homogeneous models for specific classes of coagulation kernels.
This paper establishes a complete theory of the Clifford commutant for arbitrary numbers of qubits and tensor powers by providing explicit orthogonal bases, a graphical calculus, and dimension formulas, thereby enabling new applications in magic state characterization, stabilizer property testing, and generalization to multi-qudit systems.
This paper demonstrates that in a BRST-invariant quantization of General Relativity, the bulk Hamiltonian can be expressed as a BRST-exact operator (the anticommutator of the BRST charge and the temporal ghost field), which governs time-reparameterization of physical observables without trivializing the time evolution of gravitational backgrounds or scattering amplitudes.
This paper utilizes the path integral formalism and an approximation for the centrifugal term to derive the energy spectrum and wave functions for a linear combination of Yukawa and four-parameter diatomic potentials, subsequently employing these results to calculate the system's partition function and thermodynamic properties.
This paper presents evidence supporting a conjectured connection between the absorption times of discrete Whittaker processes and the maximal heights of non-intersecting Brownian bridges.
This paper presents a unified computational framework using algebraic geometry and numerical topology to analyze the vacuum structure of 4-charge extremal black holes in Type IIA string theory, successfully reproducing BPS degeneracies for specific D-brane configurations and demonstrating the absence of zero-energy ground states in non-BPS systems through advanced topological regularization techniques.
This paper derives the effective Hamiltonian for open quantum systems with varying particle number from first principles, establishing a rigorous physico-mathematical model that proves the Hamiltonian's uniqueness, validates the surface-to-volume ratio approximation, and demonstrates that the system's Hilbert space must be isomorphic to Fock space.
This paper introduces differential operators that relate higher-Wronskian-index solutions to lower-index ones, providing an efficient method to classify rational conformal field theory characters and quasi-characters across the Wronskian tower while preserving modular covariance and integrality.