STRING QUANTIZATION IN CURVED SPACETIMES: NULL STRING APPROACH

We study quantum strings in strong gravitational fields. The relevant small parameter is where Rc is the curvature of the spacetime and T0 is the string tension. Within our systematic expansion we obtain to zeroth-order the null string (string with zero tension), while the first-order correction incorporates the string dynamics. We apply our formalism to quantum null strings in de Sitter spacetime. After a reparametrization of the worldsheet coordinates, the equations of motion are simplified. The quantum algebra generated by the constraints is considered, ordering the momentum operators to the right of the coordinate operators. No critical dimension appears. It is anticipated, however, that the conformal anomaly will appear when the first-order corrections proportional to T0, are introduced.