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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Corrolation/Green's functions

**Physics Forums | Science Articles, Homework Help, Discussion**