Olomorphic Vectorbundles and Yang Mills Fields

Abstract

In terms of differential geometry a potential should be interpreted as a connection and its field as the curvature associated to the connection. In gauge theory one is lead to consider connections and curvatures in vectorbundles. The topic of these lectures is to describe the self-dual curvatures of SU(2)-connections of vectorbundles on S⁴, which are called self-dual euclidean SU(2)-Yang Mills fields. In [1] it was shown that such fields are in a one to one correspondence with certain holomorphic vectorbundles on ℙ₃(ℂ), which are now called instantonbundles. By using the theory of moduli for algebraic vectorbundles on complex projective space explicit expressions for the euclidean SU(2)-Yang Mills fields can be derived from this correspondence. This procedure is described here only in the case of the instanton number c²=1.