Instaton -- from Eric Weisstein's World of Physics

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Instaton

A solution to the self-dual Yang-Mills equations in four-dimensional Euclidean space,

Instantons are characterized by the so-called topological charge

which is an integer. For k = 1, these equations can be solved exactly (Belavin et al. 1975, t' Hooft 1976). Furthermore, for the gauge group , the instanton gauge field one-form A and its field strength F can be written in terms of quaternions , with as

where the norm of the quaternions is defined as

(Atiyah 1979, Vandoren 2000).

For arbitrary instanton number k, the instanton solutions cannot be written down explicitly. However, it is possible to write down the solutions implicitly using the ADHM formalism (Atiyah et al. 1978).

In 1982, S. Donaldson applied instatons and the self-dual Yang-Mills equations to exotic four-dimensional spaces.

Yang-Mills Equations

References