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対角部分群

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対角部分群(diagonal subgroup)

対角部分群とは,ある群$G$の直積$G^n=G\times \cdots \times G$の部分群のうち群$G$の同一の要素からなるもの.

例)
$G = \set{(L,R)|L \in {\rm SU}(N),~R \in {\rm SU}(N) }$に対して部分群$H=\set{(V,V)|V \in {\rm SU}(N)}$は$G$の対角部分群である.ここで${\rm SU}(N)$は特殊ユニタリー群とした.

おわり

説明している文献を見つけられなかったのでメモ.QCDのカイラル対称性とその自発的破れを非線形表現で調べるときに役立つかも.

詳しい方からのコメント等頂けると大変ありがたいです.

参考文献

[1] A. Pich, "Effective Field Theory", arXiv:hep-ph/9806303, (1998).

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