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Unformatted text preview: with antisymmetric structure constants f abc . (a) (5 pts) Prove the Jacobi identity [ X a , [ X b , X c ]] + [ X b , [ X c , X a ]] + [ X c , [ X a , X b ]] = 0 by expanding out the commutators. (b) (5 pts) Use the commutation relation (2) for X a ’s in the Jacobi identity to show that f bcd f ade + f abd f cde + f cad f bde = 0 , which is also often referred to as the Jacobi identity. 3. (5 pts) Using GellMann matrices (and their commutators) Fnd the structure constants f 156 and f 678 of the group SU (3). 4. Using Young tableaux method decompose the following product representations of the group SU (3) into sums of irreducible representations: (a) (5 pts) 8 ⊗ 8 , (b) (5 pts) 8 ⊗ 3 . 1...
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This note was uploaded on 07/28/2011 for the course PHYSICS 880.02 taught by Professor Kovchegov during the Winter '09 term at Ohio State.
 Winter '09
 Kovchegov
 Physics, Mass, Work, Photon

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