Y. Takahashi et H. Umezawa, THERMO FIELD-DYNAMICS (REPRINTED FROM COLLECTIVE-PHENOMENA, VOL 2, PG55-80, 1975), International journal of modern physics b, 10(13-14), 1996, pp. 1755-1805
A quantum field theory at finite temperature is presented. The tempera
ture dependent vacuum is defined such that the vacuum expectation valu
e agrees with the statistical average. The vacuum states with differen
t temperature are connected by a Bogoliubov transformation. Our formal
ism allows the use of the Feynman diagrams for the causal Green's func
tion and the Bethe-Salpeter technique for bound states at finite tempe
rature. The entropy operator is introduced.