Keldysh-Kadanoff-Baym

The effect of thermal pion fluctuations on the specific heat and the neutrino emissivity of neutron stars was discussed in [27, 28] together with other in-medium effects, see also reviews [29, 30], Neutron pair breaking and formation (PBF) neutrino process on the neutral current was studied in [31, 32] for the hadron matter. Also ref. [32] added the proton PBF process in the hadron matter and correlation processes, and ref. [33] included quark PBF processes in quark matter. PBF processes were studied by two different methods with the help of Bogolubov transformation for the fermion wave function [31, 33] and within Schwinger-Kadanoff-Baym-Keldysh formalism for nonequilibrium normal and anomalous fermion Green functions [32, 28, 29],... 

Now we review briefly the other approach. Kadanoff-Baym-Keldysh (KBK) method systematically extends the equilibrium many-body theory to the nonequilibrium case. Potentially, it is the most powerful approach. Below we give a simple introduction into the method, which is currently actively developed. 

The external potential is included in these equations. The self-energy is defined as a function or operator in the Keldysh space according to Eq. (20). obeys the Kubo-Martin-Schwinger boundary conditions (16). The ( )-projections of the Kadanoff-Baym equations can written as... 

---