Phy5670/RPA

Polarization Propagator

To study excited states in meny-fermion systems, the limit of the two-particle (tp) propagator is used

$G_{ph}(\alpha ,\beta ^{-1};\gamma ,\delta ^{-1};t-t')=\lim _{t_{\beta }\rightarrow t^{+}}\lim _{t_{\gamma }\rightarrow t'^{+}}G_{II}(\alpha t,\delta t',\beta t_{\beta },\gamma t_{\gamma })=-{\frac {i}{\hbar }}$