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Totally symmetric arbitrary spin conformal fields propagating in the flatspace of even dimension greater than or equal to four are studied. For suchfields, we develop a general ordinary-derivative light-cone gauge formalism andobtain restrictions imposed by the conformal algebra symmetries on interactionvertices. We apply our formalism for the detailed study of conformal scalar andvector fields. For such fields, all parity-even cubic interaction vertices areobtained. The cubic vertices obtained are presented in terms of dressingoperators and undressed vertices. We show that the undressed vertices of theconformal scalar and vector fields are equal, up to overall factor, to thecubic vertices of massless scalar and vector fields. Various conjectures aboutinterrelations between the cubic vertices for conformal fields in conformalinvariant theories and the cubic vertices for massless fields in Poincareinvariant theories are proposed.

General light-cone gauge approach to conformal fields and applications to scalar and vector fields