We develop a general scheme for solving the equations of motion and constraints of strings in curved spacetimes, both classically and quantum mechanically. We treat the spacetime geometry exactly and the string excitations small as compared with the energy scales of the metric. [The perturbation (dimensionless) parameter is g=√πα'/Rc where sqrt(α')=lPl is the Planck length and Rc the typical curvature radius of the geometry.] This formalism is particularly well suited to properly consider strings in the context of quantum black holes and cosmology. As an illustration we apply it to de Sitter spacetime and find the mass spectrum and vertex operator. The lower mass states are the same as in flat space up to corrections of order g2 whereas heavy states deviate significantly from the linear Regge trajectories. We find a maximum (very large) value of order 1/g2 for the quantum number N and spin J of particles. The critical dimension for bosonic strings is found to be 25 in de Sitter spacetime.
Permanent address: Groupe d'Astrophysique Relativiste, CNRS, Observatoire de Paris, Section de Meudon, F-92195 Meudon Principal Cedex, France.
de Vega Hector J.
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