Two-Dimensional Field Reduction of the General Theory of Relativity

Abstract

In the framework of general relativity theory, we consider a space-time whose metric depends on only one coordinate and time. We choose a gauge class such that all the constraint conditions of the theory of gravity as a gauge theory are explicitly solved and construct a Hamiltonian depending only on dynamical physical variables (gravitons). We show that such a Hamiltonian can be obtained from the Polyakov action for a string in an anti-de Sitter background space with a “string constant” depending on time.