A new classical solution of the Yang-Mills field equations

The classical solutions of conformal invariant field theories have been the object of several interesting recent investigations. Two important examples are the neutral scalar field equation and the Yang-Mills equation. In the first case the classical solution has been suggested recently. On the other hand the 'instanton' solution of the latter has received a great amount of interest. The similarity between these solutions has a deep group theoretical origin. It has indeed been shown that they are both invariant under an O(5) subgroup of the O(5, 1) (Euclidean) conformal group. The beautiful and exciting features of the classical solutions are suggesting that a systematic investigation of a larger class of classical solutions might lead to a more general understanding of the properties of non-Abelian field theories. In this direction, the authors wish to point out the existence of a different kind of solutions of the conformal invariand, whose properties are in a certain way complementary to the solutions. (Auth.)