  We reconsider the construction of exponential fields in the quantized
Liouville theory. It is based on a free-field construction of a continuous
family or chiral vertex operators. We derive the fusion and braid relations of
the chiral vertex operators. This allows us to simplify the verification of
locality and crossing symmetry of the exponential fields considerably. The
calculation of the matrix elements of the exponential fields leads to a
constructive derivation of the formula proposed by Dorn/Otto and the brothers
Zamolodchikov.
