LOOP CORRECTIONS IN THE SPECTRUM OF 2-DIMENSIONAL HAWKING RADIATION

We determine the one-and two-loop backreaction corrections in the spec trum of the Hawking radiation for the Callan-Giddings-Harvey-Strominge r (CGHS) model of two-dimensional dilaton gravity by evaluating the Bo goliubov coefficients for a massless scalar field propagating on the c orresponding backgrounds. Since the backreaction can induce a small sh ift in the position of the classical horizon, we find that a positive shift leads to a non-Planckian late-time spectrum, while a null or a n egative shift leads to a Planckian late-time spectrum in the leading-o rder stationary-point approximation. In the one-loop case them are no corrections to the classical Hawking temperature, while in the two-loo p case the temperature is three times greater than the classical value . We argue that these results are consistent with the behaviour of the Hawking Bur obtained from the operator quantization only for times wh ich are not too late, in accordance with the limits of validity of the semiclassical approximation.