Why does virtually every textbook and paper treat many-body perturbation theory at finite temperature in the grand canonical ensemble? Is it not possible to formulate a canonical theory where all thermal averages are taken over the space of N-particle states, for example for N=1? Would this break some nice properties in the grand canonical theory, such as the relations between greater and lesser Green's functions and spectral functions? Might this violate Wick's theorem in some way?

  • 1
    $\begingroup$ The two most obvious reasons are: (1) N is extremely large for almost all experiments and can easily be changed by applying voltages, and (2) because you usually use a quasiparticle basis that have a finite lifetime, so fixed N is also unphysical because that are not infinitely long lived. . $\endgroup$
    – KF Gauss
    Apr 10, 2019 at 5:48
  • $\begingroup$ It is not just perturbation theory. The grand canonical enemble is much simpler to work with almost everywhere in many body quantum systems. see this answer $\endgroup$ Apr 10, 2019 at 10:32
  • $\begingroup$ Even if you work with a single electron in an empty band with an infinite phonon bath, Mahan still uses the grand canonical formalism and eliminates mu in the analytic continuation. Can anyone explain why for this one electron problem the grand canonical ensemble is still used? $\endgroup$
    – Ian
    Apr 10, 2019 at 12:45


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.