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Involution-dependent constants and the cancellation of divergences in the one-loop open-string amplitude.

We recalculate the bosonic one-loop open-string scattering amplitude using the results of the bosonic one-loop closed-string amplitude. The results show explicitly how the cancellation of divergences depends upon a set of involution-dependent constants which relate the torus to the cylinder and Moebius strip. Such a set of involution-dependent constants exists at each loop level and thus provides a means with which to study the cancellation of divergences and the connection between the world sheet and internal symmetries.