Remarks on transient photon production in heavy ion collisions

In this note, we discuss the derivation of a formula that has been used in the literature in order to compute the number of photons emitted by a hot or dense system during a finite time. Our derivation is based on a variation of the standard operator-based $S$-matrix approach. The shortcomings of this formula are then emphasized, which leads to a negative conclusion concerning the possibility of using it to predict transient effects for the photon rate.