A UNIFIED FORMALISM OF THERMAL QUANTUM-FIELD THEORY

We present a comprehensive review of the most fundamental and practica l aspects of thermo-field dynamics (TFD), including some of the most r ecent developments in the field. To make TFD fully consistent, some su itable changes in the structure of the thermal doublets and the Bogoli ubov transformation matrices have been made. A close comparison betwee n TFD and the Schwinger-Keldysh closed time path formalism (SKF) is pr esented. We find that TFD and SKF are in many ways the same in form; i n particular, the two approaches are identical in stationary situation s. However, TFD and SKF are quite different in time-dependent nonequil ibrium situations. The main source of this difference is that the time evolution of the density matrix itself is ignored in SKF while in TFD it is replaced by a time-dependent Bogoliubov transformation. In this sense TFD is a better candidate for time-dependent quantum field theo ry. Even in equilibrium situations, TFD has some remarkable advantages over the Matsubara approach and SKF, the most notable being the Feynm an diagram recipes, which we will present. We will show that the calcu lations of two-point functions are simplified, instead of being compli cated, by the matrix nature of the formalism. We will present some exp licit calculations using TFD, including space-time inhomogeneous situa tions and the vacuum polarization in equilibrium relativistic QED.