# B which one of the diagrams would be forbidden in

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diagrams following from this Lagrangian.b) Which one of the diagrams would be forbidden in real QED?c) Evaluate the other two diagrams, and express the answers in terms ofs, t, u. Givethe diagrams an extra relative minus sign, because electrons are fermions.d) Now let’s put back the spin. In the non-relativistic limit, the electron spin is con-served. This should be true at each vertex, even if the photon is virtual. For eachof the 16 possible sets of spins for the 4 electrons (for example|↑↓) → |↑↑)), whichof the diagrams can contribute for each set?e) Add up all the contributions todΩfor each spin channel. Express the answer interms ofECMand the scattering angleθ. Sketch the angular distribution.3. Use the LagrangianL=12φ1squareφ112φ2squareφ2+λ2φ1(μφ2)(μφ2) +g2φ12φ2(3)to calculate the differential cross sectiondΩ(φ1φ2φ1φ2)(4)at tree level.4. * Consider a Feynman diagram that looks like a regular tetrahedron, with the externallines coming out of the 4 corners. This can contribute to22scatttering in a scalarfield theory with interactionλ4. Write down the corresponding amplitude including theappropriate symmetry factor. You can takeφto be massless. What would the symmetryfactor be for the same diagram inφ3theory without the external lines?4!φ1
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