Quantum-Corrected Bondi Mass for 2D Hawking Radiation

We derive the Hamiltonian for general semi-classical 2D dilaton gravity, beginning with the complete action including the Polyakov action and Gibbons-Hawking-York boundary term. The value of the Hamiltonian yields a generalized Brown-York quasi-local mass function, and the ADM and Bondi masses are obtained in the appropriate limits. The Bondi mass is equal to the classical mass plus a correction term given by the transformation between initial and final inertial frames. It is non-increasing and remains positive in numerical simulations.