# Hopf-algebraic renormalization of QED in the linear covariant gauge

## Abstract

In the context of massless quantum electrodynamics (QED) with a linear covariant gauge fixing, the connection between the counterterm and the Hopf-algebraic approach to renormalization is examined. The coproduct formula of Green’s functions contains two invariant charges, which give rise to different renormalization group functions. All formulas are tested by explicit computations to third loop order. The possibility of a finite electron self-energy by fixing a generalized linear covariant gauge is discussed. An analysis of subdivergences leads to the conclusion that such a gauge only exists in quenched QED.

- Authors:

- Publication Date:

- OSTI Identifier:
- 22617375

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics; Journal Volume: 372; Other Information: Copyright (c) 2016 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:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; GREEN FUNCTION; QUANTUM ELECTRODYNAMICS; RENORMALIZATION

### Citation Formats

```
Kißler, Henry, E-mail: kissler@physik.hu-berlin.de.
```*Hopf-algebraic renormalization of QED in the linear covariant gauge*. United States: N. p., 2016.
Web. doi:10.1016/J.AOP.2016.05.008.

```
Kißler, Henry, E-mail: kissler@physik.hu-berlin.de.
```*Hopf-algebraic renormalization of QED in the linear covariant gauge*. United States. doi:10.1016/J.AOP.2016.05.008.

```
Kißler, Henry, E-mail: kissler@physik.hu-berlin.de. Thu .
"Hopf-algebraic renormalization of QED in the linear covariant gauge". United States.
doi:10.1016/J.AOP.2016.05.008.
```

```
@article{osti_22617375,
```

title = {Hopf-algebraic renormalization of QED in the linear covariant gauge},

author = {Kißler, Henry, E-mail: kissler@physik.hu-berlin.de},

abstractNote = {In the context of massless quantum electrodynamics (QED) with a linear covariant gauge fixing, the connection between the counterterm and the Hopf-algebraic approach to renormalization is examined. The coproduct formula of Green’s functions contains two invariant charges, which give rise to different renormalization group functions. All formulas are tested by explicit computations to third loop order. The possibility of a finite electron self-energy by fixing a generalized linear covariant gauge is discussed. An analysis of subdivergences leads to the conclusion that such a gauge only exists in quenched QED.},

doi = {10.1016/J.AOP.2016.05.008},

journal = {Annals of Physics},

number = ,

volume = 372,

place = {United States},

year = {Thu Sep 15 00:00:00 EDT 2016},

month = {Thu Sep 15 00:00:00 EDT 2016}

}

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