A physical interpretation of cocycle factors in vertex operator representations

It is shown that cocycle factors, which appear in vertex operator representations of affine Kac-Moody algebras or in compactified closed string theories on tori and/or orbifolds, have a simple geometrical meaning and that multiplying vertex operators by cocycle factors is equivalent to modifying commutation relations for zero modes. The origin of cocycle factors is revealed in the second quantized picture. (orig.)