Super-Poincare Covariant Quantization of the Superstring

Using pure spinors, the superstring is covariantly quantized. For the first time, massless vertex operators are constructed and scattering amplitudes are computed in a manifestly ten-dimensional super-Poincar'e covariant manner. Quantizable non-linear sigma model actions are constructed for the superstring in curved backgrounds, including the $Ad{S}_5\times S^5$ background with Ramond-Ramond flux.