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In mathematics, the Chern–Simons forms are certain secondary characteristic classes. They have been found to be of interest in gauge theory, and they (especially the 3-form) define the action of Chern–Simons theory. The theory is named for Shiing-Shen Chern and James Harris Simons, co-authors of a 1974 paper entitled "Characteristic Forms and Geometric Invariants," from which the theory arose. See ==Definition== Given a manifold and a Lie algebra valued 1-form, over it, we can define a family of p-forms: In one dimension, the Chern–Simons 1-form is given by : In three dimensions, the Chern–Simons 3-form is given by : In five dimensions, the Chern–Simons 5-form is given by : where the curvature F is defined as : The general Chern–Simons form is defined in such a way that : where the wedge product is used to define ''Fk''. The right-hand side of this equation is proportional to the ''k''-th Chern character of the connection . In general, the Chern–Simons p-form is defined for any odd ''p''. See also gauge theory for the definitions. Its integral over a ''p''-dimensional manifold is a global geometric invariant, and is typically gauge invariant modulo addition of an integer. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Chern–Simons form」の詳細全文を読む スポンサード リンク
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