Physical Review D - Particles, Fields, Gravitation, and Cosmology
We examine the nonequilibrium dynamics of a self-interacting λφ4 scalar field theory. Using a real time formulation of finite temperature field theory we derive, up to two loops and O(λ2), the effective equation of motion describing the approach to equilibrium. We present a detailed analysis of the approxi- mations 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 infi- nite temperature limit. We also address the effect of couplings to other fields, which we assume play the roˆle 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.
Gleiser, Marcelo and Ramos, Rudnei O., "Microphysical Approach to Nonequilibrium Dynamics of Quantum Fields" (1993). Open Dartmouth: Faculty Open Access Scholarship. 1984.