NEGF itself is an approximation to  a given order. The idea of transfer matrix is beyond me. But to a given order every method can give similar results.

Thanks Haroon Bhai for your reply.I came to know after looking at your publication with Ahsan sir,that you people are also using NEGF approach in your work,bhai in case of Transfer matrix approach,with Green Function it is very difficult to solve the problems when we have two hoppings at the same time,so we are in positions to solve these kinds of problems with Transfer matrix methods,firstly given by as i know Krammer and Mackinon.While as you know that i case of NEGF ,if we want to include e-e interaction or even electron-phonon interaction,it can be done with Schrodinger-Poisson solver in case of Green function,while in case of NEGf we are in need of Transport equation.BTW bhaijaan ,which book you have referred for Keldysh formalism.Nice to hear you after so many days,Stay in touch 

regards

For Keldysh formalism please refer to the original paper by Keldysh entitled as  "Diagram Technique for Nonequilibrium Processes".

Further there are many books on 'electron transport in mesoscopic systems' blah-blah, kindly refer to one such.

I have a question about "How can we integrate out (Trace out ) two fermionic operators out of the four particle eigenstate, in second quantized form??? " Please reply by your help or suggestion , if you know anything about tracing out.