A diagram technique can be constructed for so-called “temperature Green’s functions”, which depend on a temperature *T,* or rather on , which varies from 0 to 1/*kT,* where *k* is Boltzmann’s constant.

One seeks a perturbation expansion of the partition function

with *β* = 1/*kT, H* the many-electron Hamiltonian, *N*_{0} the number operator for electrons, and *μ* a parameter, which may be called the “chemical potential”. The trace is taken in Fock space; *i.e.,* the summation is taken over all possible states of the system with a given number of electrons and over all numbers of electrons.

The Hamiltonian is partitioned into a reference or unperturbed part *H*_{0} and a perturbation *V* as

with

in diagonal form. The number operator in the same basis is

A partition function for the unperturbed system is

and the trace can be taken over a direct product ...

Start Free Trial

No credit card required