I am currently reading "Quantum Field Theory and the Standard model" by Matthew Schwartz, my question refers to the part were he states that we can use the LSZ theorem for any operator that can create 1-particle states, this I will not object to.

However he then goes on to give the example of using the operator $\overline{\psi_e}\psi_e$ to calculate S-matrix elements for positronium scattering or production, I do not understand why this is correct. He sort of justifies this by stating that the positronium has the same quantum numbers as the operators, and therefore they should have some non-zero overlap, but I don't get why it would give exactly the right results.

  • $\begingroup$ For those who may be interested, much reading has lead to me to think that the LSZ theorem is much more powerful than I originally thought: if I have an operator that is able to create particle states (not necessarily an elementary field operator) then it would seem that the LSZ theorem manages to project out of the greens function the right parts I want from the correlation function of that operator so that I get the S matrix element... $\endgroup$ – Jack Sep 21 '15 at 20:08

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