BPST Instanton - Other Solutions To The Field Equations

Other Solutions To The Field Equations

The instanton and anti-instantons are not the only solutions of the Wick-rotated Yang-Mills field equations. Multi-instanton solutions have been found for q equal to two and three, and partial solutions exist for higher q as well. General multi-instanton solutions can only be approximated using the valley approximation — one starts from a certain ansatz (usually the sum of the required number of instantons) and one minimizes numerically the action under a given constraint (keeping the number of instantons and the sizes of the instantons constant).

Solutions which are not self-dual also exist. These are not local minima of the action, but instead they correspond to saddle points.

Instantons are also closely related to merons, singular non-dual solutions of the Euclidian Yang-Mills field equations of topological charge 1/2. Instantons are thought to be composed of two merons.

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