H. Chu et H. Umezawa, STABLE QUASI-PARTICLE PICTURE IN THERMAL QUANTUM-FIELD PHYSICS, International journal of modern physics A, 9(10), 1994, pp. 1703-1729
It is well known that physical particles are thermally dissipative at
finite temperature. In this paper we reformulate both the equilibrium
and nonequilibrium thermal field theories in terms of stable quasipart
icles. We will redefine the thermal doublets, the double tilde conjuga
tion rules and the thermal Bogoliubov transformations so that our theo
ry can be consistent for most general situations. All operators, inclu
ding the dissipative physical particle operators, are realized in a Fo
ck space defined by the stable quasiparticles. The propagators of the
physical particles are expressed in terms of the operators of such sta
ble quasiparticles, which is a simple diagonal matrix wi th the diagon
al elements being the temporal step functions, same as the propagators
in the usual quantum field theory without thermal degrees of freedom.
The proper self-energies are also expressed in terms of these stable
quasiparticle propagators. This formalism inherits the definition of o
n-shell self-energy in the usual quantum field theory. With this defin
ition, a self-consistent renormalization is formulated which leads to
quantum Boltzmann equation and the entropy law. With the aid of a doub
let vector algebra we have an extremely simple recipe for computing Fe
ynman diagrams. We apply this recipe to several examples of equilibriu
m and nonequilibrium two-point functions, and to the kinetic equation
for the particle numbers.