The Geometry of Self-Dual Gauge Fields
نویسندگان
چکیده
Self-dual 2-forms in D = 2n dimensions are characterised by an eigenvalue criterion. The equivalence of various definitions of selfduality is proven. We show that the self-dual 2-forms determine a n − n + 1 dimensional manifold S2n and the dimension of the maximal linear subspaces of S2n is equal to the Radon-Hurwitz number of linearly independent vector fields on the sphere S. 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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