The phase space methods in QFT

Abstract

In this chapter we investigate a Lindblad type of dissipation in a canonical relativistic quantum field theory (QFT). The classical state is defined by a probability measure on the phase space, whereas an arbitrary integrable function defined on the phase space can be considered as an observable. There is a need for a dissipative quantum theory arising from a quantum field theory of the Josephson junction, in which dissipation phenomena play an important role [245] [110][384]. The need to generalize the quantum state reduction model discussed in Chapter 12 to a relativistic quantum field theory supplies another motivation for a Wigner function approach. As shown in section 14.5 the limit ℏ → 0 is much smoother in a mixed state with a dissipation of the Lindblad type. We reformulate in this chapter the quantum field theory in terms of the Wigner distribution. We prove that the classical limit of the quantum dynamics leads to a dissipative dynamics of classical field theory. The dissipation may involve either a thermal reservoir or an interaction with a classical environment corresponding to a field measurement.