`Perturbative Non-Equilibrium Thermal Field Theory'

Abstract:
We present a novel and fully perturbative formulation of non-equilibrium
thermal field theory, applicable to the description of ultra-relativistic
many-body systems across a range of disciplines. The diagrammatic perturbation
series are built from non-homogeneous free propagators and explicitly
time-dependent vertices, which together encode the absolute space-time
dependence of the statistical background. This perturbative expansion is free
of so-called pinch singularities, without ad hoc prescription or effective
resummation of finite widths. Thus, this new approach does not suffer the
mathematical pathologies previously thought to spoil truly perturbative
treatments of non-equilibrium field theory. Arriving at a physically
meaningful definition of particle number densities that does not rely on
quasi-particle approximation, we derive master time evolution equations for
statistical distribution functions, valid to all orders in perturbation theory
and all orders in a gradient expansion. Truncating these transport equations
in a perturbative loopwise sense, we successfully capture evolution on all
timescales. Finally, with reference to a scalar model, we show that transient
early-time behaviour is dominated by non-Markovian energy-violating processes,
resulting from the systematic inclusion of finite-time effects.