The Geometry of SelfDual Gauge Fields
Abstract
Selfdual 2forms in D=2n dimensions are characterised by an eigenvalue criterion. The equivalence of various definitions of selfduality is proven. We show that the selfdual 2forms determine a n^2n+1 dimensional manifold S_{2n} and the dimension of the maximal linear subspaces of S_{2n}$ is equal to the RadonHurwitz number of linearly independent vector fields on the sphere S^{2n1}. 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 selfdual 2forms is given. The construction of the octonionic instanton solution in D=8 dimensions is discussed.
 Publication:

arXiv eprints
 Pub Date:
 December 1996
 DOI:
 10.48550/arXiv.hepth/9612230
 arXiv:
 arXiv:hepth/9612230
 Bibcode:
 1996hep.th...12230B
 Keywords:

 High Energy Physics  Theory
 EPrint:
 14 pages, Latex (No figures) Paper presented to The 9th Max Born Symposium, Karpacz, Poland 2527 September 1996