HW12 - PHY5667 Problem Set#12(Last HW(10 points total due...

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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 φ and a left-handed spinor ψ L : L = ( ∂ μ φ * )( ∂ μ φ )- m 2 φ * φ + i ψ † L ¯ σ μ ∂ μ ψ L- λφψ T L i σ 2 ψ L + λφ * ψ † L i σ 2 ψ * L , where λ is a real constant. (i) This Lagrangian possesses one U(1) symmetry. Assuming that φ has charge 1, i.e., the U(1) transforms φ as φ → φ = e i α φ , identify the U(1) transformation on ψ L . What is the U(1) charge of ψ L ? (ii) Derive the conserved Noether current J μ for the U(1). (iii) Verify that the current is conserved, ∂ μ J μ = 0, by using the equations of motion. (iv) This theory also possesses a CP symmetry. Assuming that ψ transforms under CP as ψ L ( t,~x ) → ψ L ( t,~x ) = i σ 2 ψ * L ( t,- ~x ) , determine the CP phase of φ , i.e., η in φ ( t,~x ) → φ ( t,~x ) = ηφ * ( t,- ~x )....
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HW12 - PHY5667 Problem Set#12(Last HW(10 points total due...

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