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In theoretical physics and mathematics, the Wess–Zumino–Witten (WZW) model, also called the Wess–Zumino–Novikov–Witten model, is a simple model of conformal field theory whose solutions are realized by affine Kac–Moody algebras. It is named after Julius Wess, Bruno Zumino, Sergei Novikov and Edward Witten. 〔; 〕 ==Action== Let ''G'' denote a compact simply-connected Lie group and ''g'' its simple Lie algebra. Suppose that ''γ'' is a ''G''-valued field on the complex plane. More precisely, we want ''γ'' to be defined on the Riemann sphere ''S'' ², which amounts to the complex plane compactified by adding a point at infinity. The WZW model is then a nonlinear sigma model defined by ''γ'' with an action given by : Here, is the partial derivative and the usual summation convention over indices is used, with a Euclidean metric. Here, is the Killing form on ''g'', and thus the first term is the standard kinetic term of quantum field theory. The term ''S''WZ is called the ''Wess–Zumino term'' and can be written as : where () is the commutator, is the completely anti-symmetric tensor, and the integration coordinates ''y''''i'' for ''i''=1,2,3 range over the unit ball ''B'' ³. In this integral, the field γ has been extended so that it is defined on the interior of the unit ball. This extension can always be done because the homotopy group π2 (''G'') always vanishes for any compact, simply-connected Lie group, and we originally defined ''γ'' on the 2-sphere ''S'' ² = ∂''B'' ³. 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「Wess–Zumino–Witten model」の詳細全文を読む スポンサード リンク
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