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Unformatted text preview: Homework Set No. 4, Physics 880.08 Deadline – noon on Tuesday, March 15, 2011 1. Construct the momentum-space Feynman rules for the following theories (draw all the propagators and vertices, and find their contributions to the diagrams): a. (10 pts) Scalar electrodynamics, with the Lagrangian density L = ( D μ ϕ ) * D μ ϕ- m 2 ϕ * ϕ- 1 4 F μν F μν , where D μ = ∂ μ + i eA μ . Here ϕ is a complex scalar field, A μ is a real gauge field, F μν = ∂ μ A ν- ∂ ν A μ . b. (5 pts) Complex scalar theory, with the Lagrangian density L = ( ∂ μ ϕ ) * ∂ μ ϕ- λ 2 ϕ * ϕ ( ϕ * ϕ- v 2 ) 2 , where λ and v are real positive constants and ϕ is a complex scalar field. Note that while for the photon propagator you can simply use the expression given in class, I would like you to derive the propagator for the complex scalar field in part a . 2. Consider ϕ 4 scalar theory with the Lagrangian L = 1 2 ∂ μ ϕ ∂ μ ϕ- m 2 2 ϕ 2- λ 4!...
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