Finite Action Yang-Mills Solutions on the Group Manifold

Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology

Scientific paper

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10 pages LaTeX (REVTeX3.0, No Figures), To appear in J. Physics A: Mathematical and General

Scientific paper

10.1088/0305-4470/29/16/021

We demonstrate that the left (and right) invariant Maurer-Cartan forms for any semi-simple Lie group enable one to construct solutions of the Yang-Mills equations on the group manifold equipped with the natural Cartan-Killing metric. For the unitary unimodular groups the Yang-Mills action integral is finite for such solutions. This is explicitly exhibited for the case of $SU(3)$.

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