Derivation of the one-particle Green's function?

[gluons]

Hello,

I am looking for a good reference book that has a detailed derivation of the single particle Green's function. I expected this to be in Sakurai but it's not. I couldn't find the spectral representation of this simple function in Ashcroft or any other solid state book either. Jackson has plenty on Green's functions for charged systems but I'd like to use a quantum text with bracket notation of some kind.

Basically I am looking for some thorough treatment of the resolvent of the single particle Hamiltonian and the representations of the Green's function. What text would you recommend?

 

[Bill_K]

Assuming you mean the Green's functions for the Klein-Gordon equation and the Dirac equation, a good treatment can be found in Bjorken and Drell vol II, Appendix C.