# Gauge invariance in the operator-product expansion in non-Abelian gauge theory. [Ward-Takahashi identities]

## 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. (AIP)

- Authors:

- Publication Date:

- Research Org.:
- Department of Physics, University of Washington, Seattle, Washington 98195

- OSTI Identifier:
- 7344699

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Phys. Rev., D; (United States); Journal Volume: 14:4

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; QUANTUM FIELD THEORY; GAUGE INVARIANCE; MATHEMATICAL OPERATORS; ASYMPTOTIC SOLUTIONS; DIMENSIONS; LIGHT CONE; RENORMALIZATION; TENSORS; WARD IDENTITY; FIELD THEORIES; INVARIANCE PRINCIPLES; SPACE-TIME; 645400* - High Energy Physics- Field Theory

### Citation Formats

```
Lee, C.
```*Gauge invariance in the operator-product expansion in non-Abelian gauge theory. [Ward-Takahashi identities]*. United States: N. p., 1976.
Web. doi:10.1103/PhysRevD.14.1078.

```
Lee, C.
```*Gauge invariance in the operator-product expansion in non-Abelian gauge theory. [Ward-Takahashi identities]*. United States. doi:10.1103/PhysRevD.14.1078.

```
Lee, C. Sun .
"Gauge invariance in the operator-product expansion in non-Abelian gauge theory. [Ward-Takahashi identities]". United States. doi:10.1103/PhysRevD.14.1078.
```

```
@article{osti_7344699,
```

title = {Gauge invariance in the operator-product expansion in non-Abelian gauge theory. [Ward-Takahashi identities]},

author = {Lee, C.},

abstractNote = {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. (AIP)},

doi = {10.1103/PhysRevD.14.1078},

journal = {Phys. Rev., D; (United States)},

number = ,

volume = 14:4,

place = {United States},

year = {Sun Aug 15 00:00:00 EDT 1976},

month = {Sun Aug 15 00:00:00 EDT 1976}

}