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253a/SchwartzDue Wed, October 3, 2018 at 5pmProblem Set 41. Consider the Lagrangian for±3theoryL=¡12±(±+m2)±+g3!±3(1)a) Draw a tree level Feynman diagram for the decay±!±±. 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 represented withDF's.d) Show that after you apply LSZ, integrating the phases into²-functions, and inte-grating over those²-functions, what you got inc)reduces to what you got inb).2. Moller scattering is the processe¡e¡!e¡e¡. If the electron and photon were spinless, inthe non-relativistic limit we can write the Lagrangian asL=¡12±e(±+me2)±e¡12A0±A0+emeA0±e±e(2)whereA0is the scalar potential and the factor ofmecomes from the non-relativistic limitas in Chapter 5 (or by dimensional analysis!).