# hw24 - Homework Set No 4 Physics 880.08 Deadline noon on...

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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 e A 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! ϕ 4 . Below use Pauli-Villars regularization with two new particles, such that the propagators of

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