RELATION BETWEEN REAL-TIME AND IMAGINARY-TIME FORMALISMS OF FINITE-TEMPERATURE QUANTUM-FIELD THEORY

Perturbative structures of finite-temperature quantum field theory are studied at a fundamental level. It is shown that the real-time formalism based on the Keldysh expansion and the imaginary-time formalism are related by a unitary transformation, and therefore are physically equivalent provided both of them are expressed in retarded form. On the other hand it is impossible for the thermo field dynamics to be reformulated in terms of retarded functions in conformity with the imaginary-time formalism due to the lack of unitary equivalence with the Keldysh and the imaginary-time formalisms which arises from its choice of path in the complex-time plane.