Local solutions of harmonical and bi-harmonical equations, Universal Field Equation and self-dual configurations of Yang--Mills fields in four dimensions

1994/03/21 by A. N. Leznov, Leznov, A. N.
Biochemistry, Genetics and Molecular Biology · Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Geomagnetism and Paleomagnetism Studies #Geophysics and Gravity Measurements #High Energy Physics - Theory (hep-th) #hep-th

paper · pdf · doi:10.48550/arxiv.hep-th/9403118

5 pages, LaTeX file, IHEP 94-21

arxiv created 1994/03/21 · openalex publication_date 1994/03/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A general method for the construction of solutions of the d'Alambertian and double d'Alambertian (harmonic and bi-harmonic) equations with local dependence of arbitrary functions upon two independent arguments is proposed. The connection between solutions of this kind and self-dual configurations of gauge fields having no singularities is established.

Related

• Manifestly invariant actions for harmonic self-dual gauge theory
• The Self-Duality Equations on a Riemann Surface
• On self-dual Yang-Mills fields in eight and seven dimensions
• Self-dual and anti-self-dual solutions of discrete Yang-Mills equations on a double complex
• Particles as singularities within the unified algebraic field dynamics