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�ySEOtext�z0. General Formulation, 3. Symmetry of Action, The action I has Poincare invariance. �̓Ó�¸R4(R4), ƒÎ�¸P1; I(ƒÎƒÓ)=I(ƒÓ), 4. Application of Noether's Theorem, {x'ƒÊ(x,ƒÃ)=[{exp[-(i/2)ƒÃƒÆƒÏƒÐMƒÏƒÐ+iƒÃaƒÏPƒÏ]}(x)]ƒÊ, ƒÓ'ƒÊ(x;ƒÓ,ƒÃ)=[{exp[-(i/2)ƒÃƒÆƒÏƒÐMƒÏƒÐ1+iƒÃaƒÏPƒÏ1]}ƒÓ]ƒÊ(x), TƒÊ(x;ƒÓ)=aƒÏƒÎƒÏƒÊ(x;ƒÓ)+(1/2)ƒÆƒÏƒÐ[-xƒÏƒÎƒÐƒÊ(x;ƒÓ)+xƒÐƒÎƒÏƒÊ(x;ƒÓ)-ƒÓƒÏ(x)(�݃ЃӃÊ(x)-�݃ʃӃÐ(x))+ƒÓƒÐ(x)(�݃σӃÊ(x)-�݃ʃӃÏ(x))] where: ƒÎƒÏƒÐ(x;ƒÓ)=gƒÏƒÐL(x;ƒÓ)+�݃σӃË(x)[�݃ЃӃË(x)-�݃˃ӃÐ(x)], {TƒÊ,ƒÏa(x;ƒÓ)=-ƒÎƒÏƒÊ(x;ƒÓ), TƒÊ,ƒÏƒÐƒÆ(x;ƒÓ)=-xƒÏƒÎƒÐƒÊ(x;ƒÓ)+xƒÐƒÎƒÏƒÊ(x;ƒÓ)-ƒÓƒÏ(x)[�݃ЃӃÊ(x)-�݃ʃӃÐ(x)]+ƒÓƒÐ(x)[�݃σӃÊ(x)-�݃ʃӃÏ(x)] |
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