Applications of hypercomplex automorphic forms in Yang-Mills gauge theories

Rolf Sören Kraußhar and Jürgen Tolksdorf

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Submission date: 04. Oct. 2013
Pages: 20
published in: Complex analysis and operator theory, 9 (2015) 2, p. 431-444 
DOI number (of the published article): 10.1007/s11785-014-0374-2
Bibtex
MSC-Numbers: 30G35, 70S15
PACS-Numbers: 11.15.-q, 02.30.-f
Keywords and phrases: Yang-Mills Theory, hypercomplex automorphic forms, conformally flat manifolds
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Abstract:
n 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 DΔf = 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.