Hi all, this is a question about Green's functions (sometimes called corrolation functions), used in the LSZ reduction formula. They are defined in section 3.7 of http://www.damtp.cam.ac.uk/user/tong/qft/three.pdf in two different (but equivalent) ways:(adsbygoogle = window.adsbygoogle || []).push({});

G^{(n)}(x_{1}, x_{2}...x_{n}):= <[itex]\Omega[/itex]|T{[itex]\Phi[/itex]_{1H}[itex]\Phi[/itex]_{2H}...[itex]\Phi[/itex]_{nH}}|[itex]\Omega[/itex]> = <0|T{[itex]\Phi[/itex]_{1}[itex]\Phi[/itex]_{2}...[itex]\Phi[/itex]_{n}}S|0>/<0|S|0> = sum of all connected Feynman graphs (where |[itex]\Omega[/itex]> is the true vacuum of the interacting theory, normalized to H|[itex]\Omega[/itex]> = 0; [itex]\Phi[/itex]_{nH}= [itex]\Phi[/itex](x_{n}) in the Heisenberg picture; T is the time-ordering operator and S is the scattering matrix). The link above has a very nice proof that these are all equivalent, but my question is: how, then, does one define the correlation functions for a theory where NOT all the operators are the same? At a guess, it would be defined as the above with a different choice of field operators as each combination for the LSZ formula requires...can anyone verify this or else tell me how such objects are calculated or where I can find out more?

Also, if anyone can point me in the direction of some resources where some of the phenomena mentioned related to Green's functions are calculated?

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# Corrolation/Green's functions

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