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We canonically quantize closed string theory in the pp-wave background with anon-zero flux of the three-form field strength by using the covariant BRSToperator formalism. In this canonical quantization, we completely construct newcovariant free-mode representations, for which it is particularly important totake account of the commutation relations of the zero mode of the light-conestring coordinate X^{-} with other modes. All covariant string coordinates arecomposed of the free-modes. Moreover, employing these covariant stringcoordinates for the energy-momentum tensor, we calculate the anomaly in theVirasoro algebra and determine the number of dimensions of spacetime and theordering constant from the nilpotency condition of the BRST charge in thepp-wave background.Comment: 30 page

Covariant BRST Quantization of Closed Strings in the pp-Wave Background