Using second-rank tensor field variablesϕμν and requiring that the theory be derivable from a Lagrangian variational principle (and consequentially can be quantized), it is shown that the theory is restricted to the case in which the field variables are taken to be symmetrica priori, and in which the field equations, commutators, propagators and energy-momentum tensor are uniquely determined, although all derived from a single-parameter family of Lagrangians. Conventional normalization of the field variable suggests that the propagators currently used in f0-meson theory be halved. It is not possible, as it is in the massive spin-1 case, to determine the Lagrangian uniquely by postulating conventional canonical commutation relations, although the requirement of maximum simplicity in these relations does give a preferred Lagrangian.