Gauge invariance in the operator-product expansion in non-Abelian gauge theory

Abstract

Non-gauge-invariant operators appear in addition to manifestly gauge-invariant operators in the operator-product expansion in non-Abelian gauge theories. However, with the help of various Ward-Takahashi identities, it is shown that these operators which are not gauge invariant do not mix with the gauge-invariant operators to all orders in perturbation theory. These "null" operators have vanishing matrix elements in the physical subspace. Accordingly, the null operators may be neglected completely in the operator-product expansion, and the anomalous dimensions of gauge-invariant operators can be found by simply examining the mixing between the gauge-invariant operators if the correct separation between the gauge-invariant operators and the null operators is made. Our discussion is restricted to the light-cone-dominant twist-two operators with arbitrary spin.