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Unformatted text preview: Physics 651 Problem Set 8 (due 11/03/03) Read the rest of Chapter 3. 1. Consider a complex KleinGordon field ( x ) (recall earlier homework). a) Find unitary operators U ( P ), U ( C ), and an anti-unitary operator U ( T ) (all defined in terms of their action on the annihilation operators a p and b p for the KleinGordon particles and antiparticles) that give the following transformations of the field: U ( P ) ( x , t ) U- 1 ( P ) = (- x , t ) , U ( C ) ( x , t ) U- 1 ( C ) = * ( x , t ) , U ( T ) ( x , t ) U- 1 ( T ) = ( x ,- t ) . b) Find the transformation properties of the components of the current j = i [ * - ( * ) ] under P , C , and T . 2. Derive Eq.(3.126), (3.139) and (3.145). Also derive Eq.(3.129), (3.141) and (3.147). 3. Using Table in p.71 and what you know, show that the usual (renormalizable) action S for ( x ), ( x ), and their conjugates has CPT = +1....
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