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Unformatted text preview: Homework Set No. 3, Physics 880.02 Deadline Tuesday, February 17, 2009 1. Just like in class consider 2flavor QCD with massless quarks: q ( x ) = u ( x ) d ( x ) , q L,R = 1 5 2 q. The Lagrangian is L = q L i q L + q R i q R . The left and righthanded isospin currents are j i L = q L i 2 q L and j i R = q R i 2 q R with the charges Q i L ( t ) = Z d 3 x j i L, ( ~x, t ) and Q i R ( t ) = Z d 3 x j i R, ( ~x, t ) . a. (10 pts) Using anticommutation relations n q a ( ~x, t ) , q b ( ~x , t ) o = ab ( ~x ~x ) show that for any matrices 1 and 2 (which are matrices both in Dirac and flavor spaces) the following relation holds q ( ~x , t ) 1 q ( ~x , t ) , q ( ~x, t ) 2 q ( ~x, t ) = ( ~x ~x ) q ( ~x, t ) [ 1 , 2 ] q ( ~x, t ) . b. (10 pts) Using the result of part a show that Q i L and Q i R form a chiral algebra of SU (2) L SU (2) R , i.e., prove that Q i L , Q j...
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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, Current, Mass, Work

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