  Totally symmetric arbitrary spin conformal fields propagating in the flat
space of even dimension greater than or equal to four are studied. For such
fields, we develop a general ordinary-derivative light-cone gauge formalism and
obtain restrictions imposed by the conformal algebra symmetries on interaction
vertices. We apply our formalism for the detailed study of conformal scalar and
vector fields. For such fields, all parity-even cubic interaction vertices are
obtained. The cubic vertices obtained are presented in terms of dressing
operators and undressed vertices. We show that the undressed vertices of the
conformal scalar and vector fields are equal, up to overall factor, to the
cubic vertices of massless scalar and vector fields. Various conjectures about
interrelations between the cubic vertices for conformal fields in conformal
invariant theories and the cubic vertices for massless fields in Poincare
invariant theories are proposed.
