Variational multi-time Green's functions for nonequilibrium quantum fields

The time-dependent variational principle proposed by Ballan and Veneroni is used to provide an optimal value of the generating functional for the multi-time Green's functions of a set of bosonic observables Q(mu). By restricting the two trial quantities to gaussian operators, an explicit formula is derived for the two-time Green's function, obtained to second order through the expansion in the sources. This leads to a tractable formalism for quantum fields out of equilibrium. As an illustration, we look at the finite temperature Phi(4)-theory in curved space with coupling to gravity. (C) 1998 Academic Press.