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Physics often deals with classical models where the dynamical variables are a collection of functions ''α'' over a d-dimensional space/spacetime manifold ''M'' where ''α'' is the "flavor" index. This involves functionals over the ''φs, functional derivatives, functional integrals, etc. From a functional point of view this is equivalent to working with an infinite-dimensional smooth manifold where its points are an assignment of a function for each ''α'', and the procedure is in analogy with differential geometry where the coordinates for a point ''x'' of the manifold ''M'' are ''φ''''α''(''x''). In the DeWitt notation (named after theoretical physicist Bryce DeWitt), φ''α''(''x'') is written as φ''i'' where ''i'' is now understood as an index covering both ''α'' and ''x''. So, given a smooth functional ''A'', ''A'',''i'' stands for the functional derivative : as a functional of ''φ''. In other words, a "1-form" field over the infinite dimensional "functional manifold". In integrals, the Einstein summation convention is used. Alternatively, : ==References== * 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「DeWitt notation」の詳細全文を読む スポンサード リンク
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