A geometria e os instantons da teoria de Yang &Mills SU(2)




Classical Yang &Mills Theory is presented from a geometrical viewpoint. Many arguments leading to the "physical reality" of Yang &Mills potentials are given. Further, we specialize to SU(2) Lie group theory over Euclidean space-time. Instantons of this theory are defined and a way to compute them is shown. It is also given an introduction to Homotopy theory, starting from the very basic concepts and leading to exact sequences of fiber spaces and to some important results about the homotopy of spheres. The construction of S3-bundles over S4 representants given in [Rigas] is presented. Such mathematical objects are shown to be the natural place of instanton solutions of this theory. We adapt this construction and show how to find the fundamental instanton and anti-instanton solutions and also we give some possible ways to obtain the generalizations of this result to find multi-instantons


instantons campos de calibre (fisica) espaços fibrados (matematica)

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