Abstract
We consider the higher- (integer-)spin fields which can be realized with the derivatives of two-boson free fields in two-dimensional conformal quantum field theory. We show that the operator-product expansion (OPE) between higher-spin fields themselves cannot be closed when the spins are larger than 3. Thus, with the requirement of the closure of the OPE, the spin-3 field given by Fateev and Zamolodchikov is uniquely possible---that is, it is complete.'' The same analyses on {ital N}- ({ge}3-) boson free-field-realized conformal field theories are discussed.
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