Transport or kinetic equations are often derived assuming a quasi-particle
(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 presence of strong qualitative changes in the effective
particle distribution. These results may be used to make further analytical
progress towards a quantum Boltzmann equation including off-shell effects and a
nonzero width.Comment: 20 pages with 6 eps figures, explanation and references added; to
appear in Phys.Rev.