PS4.pdf - 253a\/Schwartz Due October 5 2010 Problem Set 4 1 Consider the Lagrangian for \u03c63 theory 1 g L = \u2212 \u03c6(\u0003 m2)\u03c6 \u03c63 2 3(1 \u0001 a Draw a tree level

PS4.pdf - 253a/Schwartz Due October 5 2010 Problem Set 4 1...

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253a/Schwartz Due October 5, 2010 Problem Set 4 1. Consider the Lagrangian for φ3theoryL=12φ(square+m2)φ+g3!φ3(1)a) Draw a tree level feynman diagram for the decayφφφ. Write down the corre-sponding amplitude using the Feynman rules.b) Now consider the one loop correction, given byWrite down the corresponding amplitude using the Feynman rules.c) Now start over and write down the diagram from partbin position space, in termsof integrals over the intermediate points and Wick contractions, represented withDFs.d) Show that after you apply LSZ, what you got inc)reduces to what you got inb),by integrating the phases intoδ-functions, and integrating over thoseδ-functions.2. Non-relatavistic Moller scattering:eeee. If the electron and photon were spinless,we can write the Lagrangian asL=12φe(square+me2)φe12AsquareA+e2meeφe(2)the factor ofmecomes from the non-relativistic limit (or by dimensional analysis!).a) Draw the three tree-leveleeeediagrams following from this Lagrangian.
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