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MiS Preprint

Applications of hypercomplex automorphic forms in Yang-Mills gauge theories

Rolf Sören Kraußhar and Jürgen Tolksdorf


In this paper we show how hypercomplex function theoretical objects can be used to construct explicitly self-dual $SU(2)$-Yang-Mills instanton solutions on certain classes of conformally flat $4$-manifolds. We use a hypercomplex argument principle to establish a natural link between the fundamental solutions of $D \Delta f = 0$ and the second Chern class of the $SU(2)$ principal bundles over these manifolds. The considered base manifolds of the bundles are not simply-connected, in general. Actually, this paper summarizes an extension of the corresponding results of Gürsey and Tze on a hyper-complex analytical description of $SU(2)$ instantons. Furthermore, it provides an application of the recently introduced new classes of hypercomplex-analytic automorphic forms.

Oct 4, 2013
Oct 17, 2013
MSC Codes:
30G35, 70S15
11.15.-q, 02.30.-f
Yang-Mills Theory, hypercomplex automorphic forms, conformally flat manifolds

Related publications

2015 Repository Open Access
Rolf Sören Krausshar and Jürgen Tolksdorf

Applications of hypercomplex automorphic forms in Yang-Mills gauge theories

In: Complex analysis and operator theory, 9 (2015) 2, pp. 431-444