, Volume 16, Issue 8, pp 561-565

Solutions of the Maxwell and Yang-Mills equations associated with hopf fibrings

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It is shown that the magnetic pole of lowest strength and the pseudoparticle solution of the Yang-Mills equations correspond to natural connections defined on the principal bundlesU(2)/U(1)=S 3S 2 andSp(2)/Sp(1)=S 7S 4, respectively. This observation leads to a general methods of constructing new, topologically nontrivial solutions of the Maxwell and Yang-Mills equations. Among them is an “electromagnetic instanton” defined over the two-dimensional complex projective space endowed with the Fubini-Study metric.

On leave from the Institute of Theoretical Physics, Warsaw University, Hoza 69, Warsaw, Poland.