Quantum gravity and superstrings: Applications to cosmology and quantization of superstrings

Three problems are investigated in this thesis. In chapter one the author derives the conditions for the existence of integral constraints on energymomentum perturbations in an arbitrary background spacetime using a covariant formalism. In chapter two, Polyakov's two dimensional model of gravity in light-cone gauge is extended to both N = 1/2 and N = 1 supersymmetric cases. Finally in chapter three the author performs a BRST quantization for the Type II Green-Schwarz string. It is found that a quadratic ghost interaction is sufficient for the truncation proposed by Kallosh and Rahmanov. The cancellation of the conformal anomaly in ten dimension is also shown