We study the covariant quantization of the Green-Schwarz (GS) superstrings proposed recently by Berkovits. In particular, we reformulate the Berkovits approach in a way that clarifies its relation with the GS approach and allows to derive in a straightforward way its extension to curved spacetime background. We explain the procedure working explicitly in the case of the heterotic string. (C) 2001 Elsevier Science B.V. All rights reserved. [References: 26]
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