# Electrodynamics of massless charged particles

## Abstract

We derive the classical dynamics of massless charged particles in a rigorous way from first principles. Since due to ultraviolet divergences this dynamics does not follow from an action principle, we rely on (a) Maxwell’s equations, (b) Lorentz- and reparameterization-invariance, and (c) local conservation of energy and momentum. Despite the presence of pronounced singularities of the electromagnetic field along Dirac-like strings, we give a constructive proof of the existence of a unique distribution-valued energy-momentum tensor. Its conservation requires the particles to obey standard Lorentz equations and they experience, hence, no radiation reaction. Correspondingly, the dynamics of interacting classical massless charged particles can be consistently defined, although they do not emit bremsstrahlung end experience no self-interaction.

- Authors:

- Dipartimento di Fisica e Astronomia, Università degli Studi di Padova, Padova, Italy and INFN, Sezione di Padova, Via F. Marzolo, 8, 35131 Padova (Italy)

- Publication Date:

- OSTI Identifier:
- 22403109

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 2; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BREMSSTRAHLUNG; CHARGED PARTICLES; ELECTRODYNAMICS; ELECTROMAGNETIC FIELDS; ENERGY-MOMENTUM TENSOR; PARTICLES; ULTRAVIOLET DIVERGENCES

### Citation Formats

```
Lechner, Kurt, E-mail: kurt.lechner@pd.infn.it.
```*Electrodynamics of massless charged particles*. United States: N. p., 2015.
Web. doi:10.1063/1.4906813.

```
Lechner, Kurt, E-mail: kurt.lechner@pd.infn.it.
```*Electrodynamics of massless charged particles*. United States. doi:10.1063/1.4906813.

```
Lechner, Kurt, E-mail: kurt.lechner@pd.infn.it. Sun .
"Electrodynamics of massless charged particles". United States.
doi:10.1063/1.4906813.
```

```
@article{osti_22403109,
```

title = {Electrodynamics of massless charged particles},

author = {Lechner, Kurt, E-mail: kurt.lechner@pd.infn.it},

abstractNote = {We derive the classical dynamics of massless charged particles in a rigorous way from first principles. Since due to ultraviolet divergences this dynamics does not follow from an action principle, we rely on (a) Maxwell’s equations, (b) Lorentz- and reparameterization-invariance, and (c) local conservation of energy and momentum. Despite the presence of pronounced singularities of the electromagnetic field along Dirac-like strings, we give a constructive proof of the existence of a unique distribution-valued energy-momentum tensor. Its conservation requires the particles to obey standard Lorentz equations and they experience, hence, no radiation reaction. Correspondingly, the dynamics of interacting classical massless charged particles can be consistently defined, although they do not emit bremsstrahlung end experience no self-interaction.},

doi = {10.1063/1.4906813},

journal = {Journal of Mathematical Physics},

number = 2,

volume = 56,

place = {United States},

year = {Sun Feb 15 00:00:00 EST 2015},

month = {Sun Feb 15 00:00:00 EST 2015}

}