Nonequilibrium time evolution of the spectral function in quantum field theory

Transport or kinetic equations are often derived assuming a quasiparticle (on-shell) representation of the spectral function. We investigate this assumption using a three-loop approximation of the 2PI effective action in real time, without a gradient expansion or on-shell approximation. For a scalar field in $1+1$ dimensions the nonlinear evolution, including the integration over memory kernels, can be solved numerically. We find that a spectral function approximately described by a nonzero width emerges dynamically. During the nonequilibrium time evolution the Wigner transformed spectral function is slowly varying, even in the presence of strong qualitative changes in the effective particle distribution. These results may be used to make further analytical progress toward a quantum Boltzmann equation including off-shell effects and a nonzero width.