Abstract
Although one has trusted that the tree-level string two-point amplitudes vanish due to the infinite volume of residual gauge symmetry, recently the non-zero string two-point amplitudes have been pointed out in the path integral formalism. We consider them in the operator formalism. We have succeeded in obtaining the non-zero two-point amplitude in an open bosonic string theory by introducing a novel mostly BRST exact operator. We then show some trials in a closed string theory.
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