Instantons

An instanton (or pseudoparticle) is a notion appearing in theoretical and mathematical physics. An instanton is a classical solution to equations of motion with a , non-zero action, either in quantum mechanics or in quantum field theory. More precisely, it is a solution to the equations of motion of the classical field theory on a Euclidean spacetime.

In such quantum theories, solutions to the equations of motion may be thought of as critical points of the action. The critical points of the action may be local maxima of the action, local minima, or saddle points. For example, the classical path (or classical equation of motion) is the path that minimizes the action and is therefore a global minimum. Instantons are important in quantum field theory because:

Mathematically, a Yang–Mills instanton is a self-dual or anti-self-dual connection in a principal bundle over a four-dimensional Riemannian manifold that plays the role of physical space-time in non-abelian gauge theory. Instantons are topologically nontrivial solutions of Yang–Mills equations that absolutely minimize the energy functional within their topological type. The first such solutions were discovered in the case of four-dimensional Euclidean space compactified to the four-dimensional sphere, and turned out to be localized in space-time, prompting the names pseudoparticle and instanton.

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