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In theoretical physics, a Fierz identity is an identity that allows one to rewrite ''bilinears of the product'' of two spinors as a linear combination of ''products of the bilinears'' of the individual spinors. It is named after Swiss physicist Markus Fierz. There is a version of the Fierz identities for Dirac spinors and there is another version for Weyl spinors. And there are versions for other dimensions besides 3+1 dimensions. Spinor bilinears can be thought of as elements of a Clifford Algebra. Then the Fierz identity is the concrete realization of the relation to the exterior algebra. The identities for a generic scalar written as the contraction of two Dirac bilinears of the same type can be written with coefficients according to the following table. For example, the V × V product can be expanded as, : Simplifications arise when the considered spinors are chiral or Majorana spinors as some term in the expansion can be vanishing. ==References== A derivation of identities for rewriting any scalar contraction of Dirac bilinears can be found in 29.3.4 of See also appendix B.1.2 in 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「Fierz identity」の詳細全文を読む スポンサード リンク
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