  Direct photon production from a quark gluon plasma (QGP) in thermal
equilibrium is studied directly in real time. In contrast to the usual S-matrix
calculations, the real time approach is valid for a QGP that formed and reached
LTE a short time after a collision and of finite lifetime ($\sim 10-20
\mathrm{fm}/c$ as expected at RHIC or LHC). We point out that during such
finite QGP lifetime the spectrum of emitted photons carries information on the
initial state. There is an inherent ambiguity in separating the virtual from
the observable photons during the transient evolution of the QGP. We propose a
real time formulation to extract the photon yield which includes the initial
stage of formation of the QGP parametrized by an effective time scale of
formation $\Gamma^{-1}$. This formulation coincides with the S-matrix approach
in the infinite lifetime limit. It allows to separate the virtual cloud as well
as the observable photons emitted during the pre- equilibrium stage from the
yield during the QGP lifetime. We find that the lowest order contribution
$\mathcal{O}(\alpha_{em})$ which does \emph{not} contribute to the S-matrix
approach, is of the same order of or larger than the S-matrix contribution
during the lifetime of the QGP for a typical formation time $\sim 1
\mathrm{fm}/c$. The yield for momenta $\gtrsim 3 \mathrm{Gev}/c$ features a
power law fall-off $\sim T^3 \Gamma^2/k^{5}$ and is larger than that obtained
with the S-matrix for momenta $\geq 4 \mathrm{Gev}/c$. We provide a
comprehensive numerical comparison between the real time and S-matrix yields
and study the dynamics of the build-up of the photon cloud and the different
contributions to the radiative energy loss. The reliability of the current
estimates on photon emission is discussed.
