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Self interacting scalar field
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[QUOTE="king vitamin, post: 5309857, member: 134222"] Schwartz has an accessible derivation of the LSZ formula fairly early on. The starting point is to write the diagrams for [tex] \langle f| \psi_1^{-} \psi_2^{-} \psi_3^{+}\psi_4^{+}|i\rangle = \langle 0|\psi_{out1}^{+} \psi_{out2}^{+} \psi_1^{-} \psi_2^{-} \psi_3^{+}\psi_4^{+}\psi_{in1}^{-} \psi_{in2}^{-}|0\rangle [/tex] where I think I'm using the same notation as you (but you might want to check it). But then the LSZ formula basically tells you to chop off the incoming and outgoing propagators, so for phi^4 theory you just get the vertex. In phi^3 theory, there is no first-order diagrams, but you can expand to second order in the coupling, and after chopping off the external propagators you still have the internal propagators, which you can see in the formula you gave in your first post. [/QUOTE]
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