Conformally covariant field equations I. first-order equations with non-vanishing mass

The connection of conformal fields with the Mackey theory is discussed. The necessary and sufficient conditions for the finite or infinite component field equation $$left( {L_mu partial ^mu + m} right)psi left( x right) = 0$$ to be conformally covariant, are derived. The conditions are then explicitly solved under very general assumptions and thus conformally covariant equations of the above type are explicitly found (Theorem 5). The circumstances under which the equation may be obtained from a Lagrangian are discussed.