hw21 - 3-theory described by the Lagrangian density L = 1 2...

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Homework Set No. 1, Physics 880.08 Deadline – Wednesday, January 19, 2011 1. Consider real scalar ϕ 4 -theory described by the Lagrangian density L = 1 2 μ ϕ∂ μ ϕ m 2 2 ϕ 2 λ 4! ϕ 4 . a. (10 pts) Draw all connected Feynman diagrams contributing to the two-point function a ψ 0 | ( x ) ϕ ( y ) | ψ 0 A at the order λ 3 . Find the symmetry factors for all the graphs. b. (15 pts) Draw all connected (= no vacuum bubbles) Feynman diagrams contributing to the four-point function a ψ 0 | ( x 1 ) ϕ ( x 2 ) ϕ ( x 3 ) ϕ ( x 4 ) | ψ 0 A up to the order λ 3 . Calculate the symmetry factors. c. (5 pts) What is the symmetry factor of the following Feynman diagram? 2. Consider real scalar
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Unformatted text preview: 3-theory described by the Lagrangian density L = 1 2 m 2 2 2 3! 3 . a. (10 pts) Draw all connected Feynman diagrams contributing to the two-point function a | T ( x ) ( y ) | A up to the order 4 . Find the symmetry factors. b. (10 pts) Draw all connected (= no vacuum bubbles) Feynman diagrams contributing to the three-point function a | T ( x 1 ) ( x 2 ) ( x 3 ) | A up to the order 3 . Calculate the symmetry factors. 1...
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