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ySEOtextz0. General Formulation, SU(2) and SO(3) are representations of each other. If U=exp(-iƃ) and R=exp(-iL) then: U-1kU=Rkll, 2. Symmetry of Action, a. Poincare Invariance, If '(x)=(Ӄ)(x) then: ̓P0; I(')=I(), b. SU(n) Invariance, If '(x)=UӃ(x) then: USU(n); I(')=I(), 3. Application of Noether's Theorem, a. n=1, '(x;,)=e-iÃ(x), x'(x;)=x, T(x;)=iӁ(x)݃ʁ(x) Here I abbreviate Tc to T. b. n=2, '(x;,)=[exp(-iÃƃ)]Ӄ(x), x'(x;)=x, T(x;)=ik[Ӄ(x)(k)݃ʃӃ(x)-݃ʃӃ(x)E(k)Ӄ(x)], T,k(x;)=-i݃ʃӁ(x)Ek(x)+i[݃ʃӁ(x)Ek(x)] |
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