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Unformatted text preview: PHY5667 Problem Set #12 (Last HW!) (10 points total, due in two weeks on Tue Nov 23) (no late HW accepted) (1) Consider the following QFT for a complex scalar and a left-handed spinor L : L = ( * )( )- m 2 * + i L L- T L i 2 L + * L i 2 * L , where is a real constant. (i) This Lagrangian possesses one U(1) symmetry. Assuming that has charge 1, i.e., the U(1) transforms as = e i , identify the U(1) transformation on L . What is the U(1) charge of L ? (ii) Derive the conserved Noether current J for the U(1). (iii) Verify that the current is conserved, J = 0, by using the equations of motion. (iv) This theory also possesses a CP symmetry. Assuming that transforms under CP as L ( t,~x ) L ( t,~x ) = i 2 * L ( t,- ~x ) , determine the CP phase of , i.e., in ( t,~x ) ( t,~x ) = * ( t,- ~x )....
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