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We consider the theory of bosonic closed strings on the flat backgroundR(25,1). We show how the BRST complex can be extended to a complex where thestring center of mass operator, x^mu_0, is well defined. We investigate thecohomology of the extended complex. We demonstrate that this cohomology has anumber of interesting features. Unlike in the standard BRST cohomology, thereis no doubling of physical states in the extended complex. The cohomology ofthe extended complex is more physical in a number of of aspects related to thezero-momentum states. In particular, we show that the ghost number onezero-momentum cohomology states are in one to one correspondence with thegenerators of the global symmetries of the background i.e., the Poincarealgebra.Comment: 41 pages, LaTe

String center of mass operator and its effect on BRST cohomology