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

Gauge invariance in the operator-product expansion in non-Abelian gauge theory 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review D American Physical Society (APS)

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

Physical Review D , Volume 14 (4) – Aug 15, 1976
22 pages

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Publisher
American Physical Society (APS)
Copyright
Copyright © 1976 The American Physical Society
ISSN
1089-4918
DOI
10.1103/PhysRevD.14.1078
Publisher site
See Article on Publisher Site

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.

Journal

Physical Review DAmerican Physical Society (APS)

Published: Aug 15, 1976

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