Abstract:
An equilibrium quasi-particle propagator possesses the simple semi-group property (obeys a multiplicative composition rule). For the exact non-equilibrium propagator, the multiplicative term is renormalized by a vertex, whose general form can be derived by a simple perturbative argument. An alternative derivation based on the gauge invariance of the 1st kind for propagators allows to show that the renormalized multiplicative rule is a non-equilibrium generalization of the usual Ward identity for equilibrium propagators. Out of equilibrium,the semi-group property becomes the basic token of a quasi-particle behavior,and the present theory permits to obtain the conditions for formation of non-equilibrium quasi-particles.