Question 3 2 of 2 presentations m illustrates the special property of the SU(2) representations, their being equivalent

Post by **answerhappygod** » Mon May 23, 2022 10:59 am

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Question 3 2 of 2 presentations m illustrates the special property of the SU(2) representations, their being equivalent to their complex every 2 x 2 unitary matrix U with unit determinant, show there exists a matrix S which connects U to its complex conjugate matrix U through the similarity transformation S-¹US=U*. b) Suppose and are the bases for the spin-4 representation of SU (2) having eigenvalues of ± for the diagonal generator T Ter and T calculate the eigenvalues of T, operating on e; and 2, respectively.
Question 3 This problem illustrates the special property of the SU (2) representations, their being equivalent to their complex conjugate representations. a) For every 2 x 2 unitary matrix U with unit determinant, show there exists a matrix S which connects U to its complex conjugate matrix U through the similarity transformation S-¹US=U*. b) Suppose ₁ and 2 are the bases for the spin- representation of SU(2) having eigenvalues of ±for the diagonal generator T3: T31=₁ and T32=2+ == calculate the eigenvalues of T3 operating on and 2, respectively.
Question 3 This problem illustrates the special property of the SU(2) representations, their being equivalent to their complex conjugate representations. a) For every 2 x 2 unitary matrix U with unit determinant, show there exists a matrix S which connects U to its complex conjugate matrix U through the similarity transformation S-¹US=U*. b) Suppose 1 and 2 are the bases for the spin- representation of SU(2) having eigenvalues of ± for the diagonal generator T3: 1 T301- 1-1 and T₁2--2₁ calculate the eigenvalues of T3 operating on i and 2, respectively.