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We examine the nonequilibrium dynamics of a self-interacting $\lambda\phi^4$scalar field theory. Using a real time formulation of finite temperature fieldtheory we derive, up to two loops and $O(\lambda^2)$, the effective equation ofmotion describing the approach to equilibrium. We present a detailed analysisof the approximations used in order to obtain a Langevin-like equation ofmotion, in which the noise and dissipation terms associated with quantumfluctuations obey a fluctuation-dissipation relation. We show that, in general,the noise is colored (time-dependent) and multiplicative (couples nonlinearlyto the field), even though it is still Gaussian distributed. The noise becomeswhite in the infinite temperature limit. We also address the effect ofcouplings to other fields, which we assume play the r\^ole of the thermal bath,in the effective equation of motion for $\phi$. In particular, we obtain thefluctuation and noise terms due to a quadratic coupling to another scalarfield.Comment: 30 pages, LaTex (uses RevTex 3.0), DART-HEP-93/0

Microphysical approach to nonequilibrium dynamics of quantum fields