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Instanton
An instanton〔Instantons in Gauge Theories. Edited by Mikhail A. Shifman. World Scientific, 1994.〕 (or pseudoparticle〔Interactions Between Charged Particles in a Magnetic Field. By Hrachya Nersisyan, Christian Toepffer, Günter Zwicknagel. Springer, Apr 19, 2007. Pg 23〕〔Large-Order Behaviour of Perturbation Theory. Edited by J.C. Le Guillou, J. Zinn-Justin. Elsevier, Dec 2, 2012. Pg. 170.〕) is a notion appearing in theoretical and mathematical physics. An instanton is a classical solution to equations of motion〔Equations of motion are grouped under three main ''types'' of motion: translations, rotations, oscillations (or any combinations of these).〕 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.
==Quantum theory==
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:
* they appear in the path integral as the leading quantum corrections to the classical behavior of a system, and
* they can be used to study the tunneling behavior in various systems such as a Yang–Mills theory.
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