Abstract
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 (kI + kI+1 + …)2, and it annihilates individual off-shell scalar λϕ3 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.
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