# Anatomy of a gauge theory

## Abstract

We exhibit the role of Hochschild cohomology in quantum field theory with particular emphasis on gauge theory and Dyson-Schwinger equations, the quantum equations of motion. These equations emerge from Hopf- and Lie algebra theory and free quantum field theory only. In the course of our analysis, we exhibit an intimate relation between the Slavnov-Taylor identities for the couplings and the existence of Hopf sub-algebras defined on the sum of all graphs at a given loop order, surpassing the need to work on single diagrams.

- Authors:

- IHES, 35 rte. de Chartres, 91440 Bures-sur-Yvette (France). E-mail: kreimer@ihes.fr

- Publication Date:

- OSTI Identifier:
- 20845946

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics (New York); Journal Volume: 321; Journal Issue: 12; Other Information: DOI: 10.1016/j.aop.2006.01.004; PII: S0003-4916(06)00024-8; Copyright (c) 2006 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ALGEBRA; DYSON REPRESENTATION; EQUATIONS OF MOTION; GAUGE INVARIANCE; LIE GROUPS; QUANTUM FIELD THEORY

### Citation Formats

```
Kreimer, Dirk.
```*Anatomy of a gauge theory*. United States: N. p., 2006.
Web. doi:10.1016/j.aop.2006.01.004.

```
Kreimer, Dirk.
```*Anatomy of a gauge theory*. United States. doi:10.1016/j.aop.2006.01.004.

```
Kreimer, Dirk. Fri .
"Anatomy of a gauge theory". United States.
doi:10.1016/j.aop.2006.01.004.
```

```
@article{osti_20845946,
```

title = {Anatomy of a gauge theory},

author = {Kreimer, Dirk},

abstractNote = {We exhibit the role of Hochschild cohomology in quantum field theory with particular emphasis on gauge theory and Dyson-Schwinger equations, the quantum equations of motion. These equations emerge from Hopf- and Lie algebra theory and free quantum field theory only. In the course of our analysis, we exhibit an intimate relation between the Slavnov-Taylor identities for the couplings and the existence of Hopf sub-algebras defined on the sum of all graphs at a given loop order, surpassing the need to work on single diagrams.},

doi = {10.1016/j.aop.2006.01.004},

journal = {Annals of Physics (New York)},

number = 12,

volume = 321,

place = {United States},

year = {Fri Dec 15 00:00:00 EST 2006},

month = {Fri Dec 15 00:00:00 EST 2006}

}

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