The Geometry of Self-Dual Gauge Fields

1996/12/24 by A. H. Bilge, Ayşe Hümeyra Bilge, Tekin Dereli +6
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebraic and Geometric Analysis #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Microtubule and mitosis dynamics #hep-th

paper · pdf · doi:10.48550/arxiv.hep-th/9612230

14 pages, Latex (No figures) Paper presented to The 9th Max Born Symposium, Karpacz, Poland 25-27 September 1996

arxiv created 1996/12/24 · openalex publication_date 1996/12/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Self-dual 2-forms in D=2n dimensions are characterised by an eigenvalue criterion. The equivalence of various definitions of self-duality is proven. We show that the self-dual 2-forms determine a n²-n+1 dimensional manifold S_2n and the dimension of the maximal linear subspaces of S_2n is equal to the Radon-Hurwitz number of linearly independent vector fields on the sphere S^2n-1. The relation between the maximal linear subspaces and the representations of Clifford algebras is noted. A general procedure based on this relation for the explicit construction of linearly self-dual 2-forms is given. The construction of the octonionic instanton solution in D=8 dimensions is discussed.

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