Effective field theory out of equilibrium: Brownian quantum fields
Abstract
The emergence of an effective field theory out of equilibrium is studied in the case in which a light field—the system—interacts with very heavy fields in a finite temperature bath. We obtain the reduced density matrix for the light field, its time evolution is determined by an effective action that includes the influence action from correlations of the heavy degrees of freedom. The nonequilibrium effective field theory yields a Langevin equation of motion for the light field in terms of dissipative and noise kernels that obey a generalized fluctuation dissipation relation. These are completely determined by the spectral density of the bath which is analyzed in detail for several cases. At T = 0 we elucidate the effect of thresholds in the renormalization aspects and the asymptotic emergence of a local effective field theory with unitary time evolution. At T\ne 0 new ‘anomalous’ thresholds arise, in particular the decay of the environmental heavy fields into the light field leads to dissipative dynamics of the light field. Even when the heavy bath particles are thermally suppressed this dissipative contribution leads to the thermalization of the light field which is confirmed by a quantum kinetics analysis. We obtain the quantum master equation and show explicitly that its solution in the field basis is precisely the influence action that determines the effective nonequilibrium field theory. The Lindblad form of the quantum master equation features time dependent dissipative coefficients. Their time dependence is crucial to extract renormalization effects at asymptotically long time. The dynamics from the quantum master equation is in complete agreement with that of the effective action, Langevin dynamics and quantum kinetics, thus providing a unified framework to effective field theory out of equilibrium.
 Publication:

New Journal of Physics
 Pub Date:
 June 2015
 DOI:
 10.1088/13672630/17/6/063017
 arXiv:
 arXiv:1503.00156
 Bibcode:
 2015NJPh...17f3017B
 Keywords:

 High Energy Physics  Phenomenology;
 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Theory;
 Quantum Physics
 EPrint:
 33 pages 4 figs, typos fixed, refs.updated, published version