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Advanced Physics Homework Help
Feynman Diagrams for Interacting Scalar Fields
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[QUOTE="MyName, post: 5975751, member: 604229"] [h2]Homework Statement [/h2] Consider four real massive scalar fields, [itex]\phi_1,\phi_2,\phi_3,[/itex] and [itex]\phi_4[/itex], with masses [itex]M_1,M_2,M_3,M_4[/itex]. Let these fields be coupled by the interaction lagrangian [itex]\mathcal{L}_{int}=\frac{-M_3}{2}\phi_1\phi_{3}^{2}-\frac{M_4}{2}\phi_2\phi_{4}^{2}[/itex]. Find the scattering amplitude for [itex]\phi_{3}\phi_{4}\rightarrow\phi_3\phi_4[/itex], to tree level. [h2]Homework Equations[/h2] I'm not really sure what to put here. [h2]The Attempt at a Solution[/h2] This honestly looks like a trick question to me. The first step is obviously to write down the relevant feynman diagrams and feynman rules to evaluate them, but I can't find a single tree level diagram for this process. A diagram would need an incoming [itex]\phi_3[/itex] and an incoming [itex]\phi_4[/itex], as well as an outgoing [itex]\phi_3[/itex] and an outgoing [itex]\phi_4[/itex]. The interaction lagrangian makes me think that we should have a vertex between a [itex]\phi_1[/itex] and two [itex]\phi_3[/itex]'s, as well as a vertex between a [itex]\phi_2[/itex] and two [itex]\phi_4[/itex]'s, but this still doesn't allow [itex]\phi_3[/itex] and [itex]\phi_4[/itex] to interact. Perhaps I am misunderstanding the meaning of tree level (I think it just means one of each type of interaction vertex), or perhaps I am just misunderstanding the interactions. Could this possibly have to do with interactions via the kinetic terms of the lagrangian? Can a tree level diagram just consist of the [itex]\phi_3[/itex] and the [itex]\phi_4[/itex] propagating along and not interacting (if yes I don't think this would contribute to the scattering), I'm not sure and would appreciate any help. I'm just feeling pretty confused at the moment. Thanks! [/QUOTE]
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Feynman Diagrams for Interacting Scalar Fields
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