We present a new perturbative formulation of non-equilibrium thermal field theory, based upon non-homogeneous free propagators and time-dependent vertices. Our approach to non-equilibrium dynamics yields time-dependent diagrammatic perturbation series that are free of pinch singularities, without the need to resort to quasi-particle approximation or effective resummations of finite widths. In our formalism, the avoidance of pinch singularities is a consequence of the consistent inclusion of finite-time effects and the proper consideration of the time of observation. After introducing a physically meaningful definition of particle number densities, we derive master time evolution equations for statistical distribution functions, which are valid to all orders in perturbation theory. The resulting equations do not rely upon a gradient expansion of Wigner transforms or involve any separation of time scales. To illustrate the key features of our formalism, we study out-of-equilibrium decay dynamics of unstable particles in a simple scalar model. In particular, we show how finite-time effects remove the pinch singularities and lead to violation of energy conservation at early times, giving rise to otherwise kinematically forbidden processes. The non-Markovian nature of the memory effects as predicted in our formalism is explicitly demonstrated.

revtex, 79 pages, 17 figures; further clarifications and extended discussion of the absence of pinch singularities included; version accepted for publication in Physical Review D