Dissipative quantum field theory -thermo field dynamics-

A general theory of thermo field dynamics in the renormalized interaction representation is presented in such a manner that the theory includes both the equilibrium and non-equilibrium situations. The significant proposal made in this paper is the concept of the spontaneous creation of dissipation. The theory is based on (i) the tilde conjugation rule, (ii) the Hamiltonian and (iii) the thermal state conditions. It is shown that, in terminology of the theory of the interaction representation, different thermal situations correspond to different choices of the renormalized Hamiltonian Ĥt in the interaction representation (and therefore, to different choices of the interaction representation) associated with the basic Hamiltonian H - H̃ of thermo field dynamics. Any thermal situation (both in equilibrium and in non-equilibrium states) is controlled by the thermal state condition which may depend on time. The renormalized Hamiltonian Ĥt contains several c-number quantities, which are to be determined by the self-consistent renormalization equations and which may depend on time. This time-dependent renormalization is a new situation which was not formulated in the Schwinger-Keldysh path-ordering formalism. The perturbative renormalization method in thermo field dynamics is reformulated from the most general viewpoint.