  Direct photons play an important role as electromagnetic probes from the
quark-gluon plasma (QGP) which occurs during ultrarelativistic heavy-ion
collisions. In this context, it is of particular interest how the finite
lifetime of the QGP affects the resulting photon production. Earlier
investigations on this question were accompanied by a divergent contribution
from the vacuum polarization and by the remaining contributions not being
integrable in the ultraviolet (UV) domain. In this work, we provide a different
approach in which we do not consider the photon number density at finite times,
but for free asymptotic states obtained by switching the electromagnetic
interaction according to the Gell-Mann and Low theorem. This procedure
eliminates a possible unphysical contribution from the vacuum polarization and,
moreover, renders the photon number density UV integrable. It is emphasized
that the consideration of free asymptotic states is, indeed, crucial to obtain
such physically reasonable results.
