  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.
