Thermo field dynamics for quantum fields with continuous mass spectrum

Abstract

The study of quantum effects in hot, dense matter requires to account for the full spectral function of its constituents. Traditional quantum statistical methods have to be modified accordingly: Propagators and diagram rules for generalized free fields are discussed in this work, using the formalism of thermo field dynamics (TFD). This formalism is briefly reviewed at the elementary level of a single oscillator. Commuting representations of the canonical commutation relations are constructed in Liouville space, and a continuous symmetry of the time evolution generator is discussed. TFD is then applied to interacting relativistic quantum fields: The symplectic symmetry of the liouvillean is transcribed into the concept of diagonalization of the full single-particle propagator. While it leads to global equilibrium conditions for space-time homogeneous states, the diagonalization condition is equivalent to a transport equation for non-equilibrium states. To illustrate some consequences of a non-trivial spectral function on the properties of hot, dense matter, the formalism is then applied to nuclear physics: The equilibration problem in the σ-ω model is discussed, and pion propagator and transport coefficients are calculated within the Δ-hole model.