Microphysical approach to nonequilibrium dynamics of quantum fields

We examine the nonequilibrium dynamics of a self-interacting λ${\mathrm{\phi }}^4$ scalar field theory. Using a real time formulation of finite temperature field theory we derive, up to two loops and O(${\lambda }^2$), the effective equation of motion describing the approach to equilibrium. We present a detailed analysis of the approximations used in order to obtain a Langevin-like equation of motion, in which the noise and dissipation terms associated with quantum fluctuations obey a fluctuation-dissipation relation. We show that, in general, the noise is colored (time dependent) and multiplicative (couples nonlinearly to the field), even though it is still Gaussian distributed. The noise becomes white in the infinite temperature limit. We also address the effect of couplings to other fields, which we assume play the role of the thermal bath, in the effective equation of motion for φ. In particular, we obtain the fluctuation and noise terms due to a quadratic coupling to another scalar field.