An instanton is a classical solution to equations of motion with a finite, 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 a theory, 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. Instantons are important in quantum field theory because (a) they appear in the path integral as the leading quantum corrections to the classical behavior of a system, and (b) they can be used to study the tunneling behavior in various systems such as a Yang–Mills theory.
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