Instanton

In mathematical physics, an instanton is a special kind of solution of a physical theory, such as Yang-Mills theory or general relativity. A solution to such a theory is a stationary point of the associated action and an instanton is an (absolute) minimum of the action.

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The Yang-Mills action on a 4-manifold M with connection A and Yang-Mills field F = dA is

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:int_M mathrm{Tr}(F wedge *F)

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For example, in the case of the gauge group U(1), F will be the electromagnetic field tensor. From the principal of stationary action, the Yang-Mills equations follow. They are

Mathematical physics: Mathematical physics is a scientific discipline aimed at studying and solving problems inspired by physics within a mathematically rigorous framework. Mathematical physics covers a very broad area of topics with the common feature that they blend pure mathematics and physics. Although mathematical p...

Yang-Mills theory: REDIRECT Yang?Mills theory...

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