gr-qc/9702040 GENERALIZED SYMMETRIES AND INVARIANT MATTER COUPLINGS IN TWO-DIMENSIONAL DILATON GRAVITY

New features of the generalized symmetries of generic two-dimensional dilaton models of gravity are presented and invariant gravity-matter couplings are introduced. We show that there is a continuum set of Noether symmetries, which contains half a de Witt algebra. Two of these symmetries are area-preserving transformations. We show that gravity-matter couplings which are invariant under area preserving transformations only contribute to the dynamics of the dilaton-gravity sector with a reshaping of the dilaton potential. The interaction with matter by means of invariant metrics is also considered. We show in a constructive way that there are metrics which are invariant under two of the symmetries. The most general metrics and minimal couplings that fulfil this condition are found. ∗Work partially supported by the Comisión Interministerial de Ciencia y Tecnoloǵıa and DGICYT. †http://www.ugr.es/ m̃navarro; [email protected]