2001/09/28 by Martin Oettel, M. Oettel, Lorenz von Smekal +3 · 16 citations
Mathematics · Physics and Astronomy · #Bethe–Salpeter equation #Bound state #Chebyshev equation #Chebyshev iteration #Chebyshev polynomials #Classical orthogonal polynomials #Covariant transformation #Eigenvalues and eigenvectors #High-Energy Particle Collisions Research #Mathematical analysis #Mathematical physics #Mathematics #Orthogonal polynomials #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Quark #Wave function #hep-ph #nucl-th
paper · pdf · doi:10.1016/s0010-4655(01)00465-9
published in Computer Physics Communications 144(1), 63-81 (Elsevier BV) · 27 pages, 3 figures; submitted to Computer Physics Communications
arxiv created 2001/09/28 · openalex publication_date 2002/03/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Baryons as relativistic bound states in 3-quark correlations are described by an effective Bethe-Salpeter equation when irreducible 3-quark interactions are neglected and separable 2-quark correlations are assumed. We present an efficient numerical method to calculate the nucleon mass and its covariant wave function in this quantum field theoretic quark-diquark model with quark-exchange interaction. Expanding the components of the spinorial wave function in terms of Chebyshev polynomials, the four-dimensional integral equations are in a first step reduced to a coupled set of one-dimensional ones. This set of linear and homogeneous equations defines a generalised eigenvalue problem. Representing the eigenvector corresponding to the largest eigenvalue, the Chebyshev moments are then obtained by iteration. The nucleon mass is implicitly determined by the eigenvalue, and its covariant wave function is reconstructed from the moments within the Chebyshev approximation.