  Properties of the SO(2,n) Yangian acting on scalar and gauge fields are
presented. This differential operator representation of the
infinite-dimensional extension of the conformal algebra SO(2,n) is proved to
satisfy the Serre relation for arbitrary spacetime dimension n for off-shell
scalar theory, but only on shell and for n=4 in the gauge theory. The SO(2,n)
Yangian acts simply on the off-shell kinematic invariants $(k_I+k_{I+1}+
...)^2$, and it annihilates individual off-shell scalar $\lambda \phi^3$
Feynman tree graphs for n=6 if the differential operator representation is
extended by graph dependent evaluation terms. The SO(2,4) Yangian level one
generators are shown to act in a compact way on pure Yang-Mills gluon tree
amplitudes. The action of the Yangian on the scattering polynomials of a CHY
formalism is also described.
