  Conformal fields in flat space-time of even dimension greater than or equal
to four are studied. Second-derivative formulation for spin 0,1,2 conformal
bosonic fields and first-derivative formulation for spin 1/2,3/2 conformal
fermionic fields are developed. For the spin 1,3/2,2 conformal fields, we
obtain gauge invariant Lagrangians and the corresponding gauge transformations.
Gauge symmetries are realized by involving Stueckelberg fields and auxiliary
fields. Realization of global conformal boost symmetries is obtained. Modified
Lorentz and de Donder gauge conditions are introduced. Ordinary-derivative
Lagrangian of interacting Weyl gravity in 4d is obtained. In our approach, the
field content of Weyl gravity, in addition to conformal graviton field,
includes one auxiliary rank-2 symmetric tensor field and one Stueckelberg
vector field. With respect to the auxiliary tensor field, the Lagrangian
contains, in addition to other terms, the Pauli-Fierz mass term. Using the
ordinary-derivative Lagrangian of Weyl gravity, we discuss interrelation of
Einstein AdS gravity and Weyl gravity via breaking conformal gauge symmetries.
Also, we demonstrate use of the light-cone gauge for counting on-shell degrees
of freedom in higher-derivative conformal field theories.
