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A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional algebra of local conformal transformations, and conformal field theories can sometimes be exactly solved or classified. Conformal field theory has important applications〔Paul Ginsparg (1989), ''Applied Conformal Field Theory''. . Published in ''Ecole d'Eté de Physique Théorique: Champs, cordes et phénomènes critiques/Fields, strings and critical phenomena'' (Les Houches), ed. by E. Brézin and J. Zinn-Justin, Elsevier Science Publishers B.V.〕 to string theory, statistical mechanics, and condensed matter physics. Statistical and condensed matter systems are indeed often conformally invariant at their thermodynamic or quantum critical points. ==Scale invariance vs. conformal invariance== While it is possible for a quantum field theory to be scale invariant but not conformally-invariant, examples are rare.〔One physical example is the theory of elasticity in two and three dimensions (also known as the theory of a vector field without gauge invariance). See 〕 For this reason, the terms are often used interchangeably in the context of quantum field theory, even though the scale symmetry group is smaller. In some particular cases it is possible to prove that scale invariance implies conformal invariance in a quantum field theory, for example in unitary compact conformal field theories in two dimensions. 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「conformal field theory」の詳細全文を読む スポンサード リンク
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