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Direct photon production from a quark gluon plasma (QGP) in thermalequilibrium is studied directly in real time. In contrast to the usual S-matrixcalculations, the real time approach is valid for a QGP that formed and reachedLTE 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 suchfinite QGP lifetime the spectrum of emitted photons carries information on theinitial state. There is an inherent ambiguity in separating the virtual fromthe observable photons during the transient evolution of the QGP. We propose areal time formulation to extract the photon yield which includes the initialstage of formation of the QGP parametrized by an effective time scale offormation $\Gamma^{-1}$. This formulation coincides with the S-matrix approachin the infinite lifetime limit. It allows to separate the virtual cloud as wellas the observable photons emitted during the pre- equilibrium stage from theyield during the QGP lifetime. We find that the lowest order contribution$\mathcal{O}(\alpha_{em})$ which does \emph{not} contribute to the S-matrixapproach, is of the same order of or larger than the S-matrix contributionduring 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 apower law fall-off $\sim T^3 \Gamma^2/k^{5}$ and is larger than that obtainedwith the S-matrix for momenta $\geq 4 \mathrm{Gev}/c$. We provide acomprehensive numerical comparison between the real time and S-matrix yieldsand study the dynamics of the build-up of the photon cloud and the differentcontributions to the radiative energy loss. The reliability of the currentestimates on photon emission is discussed.Comment: 31 pages, 12 eps figures, version to appear in PR

Are direct photons a clean signal of a thermalized quark-gluon plasma?