2D quantum dilaton gravitational Hamiltonian, boundary terms and new definition for total energy

TL;DR

This paper derives the Hamiltonian for the 2D quantum dilaton gravity RST model, clarifies boundary contributions to total energy, and reveals new effects from hidden dynamical fields on ADM and Bondi masses.

Contribution

It provides a new Hamiltonian formulation for the RST model including boundary terms and introduces a novel contribution to mass from hidden dynamical fields.

Findings

Boundary terms define total energy in the RST model.

New contribution to ADM and Bondi mass from hidden fields.

Detailed analysis of mass properties in the RST model.

Abstract

The ADM and Bondi mass for the RST model have been first discussed from Hawking and Horowitz's argument. Expressing the localized RST action in terms of the ADM formulation, the RST Hamiltonian can be derived, meanwhile keeping track of all boundary terms. Then the total boundary terms can be taken as the total energy for the RST model. It has been found that there is a new contribution to the ADM and Bondi mass from the RST boundary due to the existence of the hidden dynamical field. The ADM and Bondi mass have been discussed respectively in detail, and some new properties have been found.