# Variational principle and energy-momentum tensor for relativistic electrodynamics of point charges

## Abstract

We give a new representation as tempered distribution for the energy-momentum tensor of a system of charged point-particles, which is free from divergent self-interactions, manifestly Lorentz-invariant and symmetric, and conserved. We present a covariant action for this system, that gives rise to the known Lorentz-Dirac equations for the particles and entails, via Noether theorem, this energy-momentum tensor. Our action is obtained from the standard action for classical electrodynamics, by means of a new Lorentz-invariant regularization procedure, followed by a renormalization. The method introduced here extends naturally to charged p-branes and arbitrary dimensions.

- Authors:

- Dipartimento di Fisica, Universita degli Studi di Padova (Italy) and Istituto Nazionale di Fisica Nucleare, Sezione di Padova, Via F. Marzolo, 8, 35131 Padova (Italy). E-mail: kurt.lechner@pd.infn.it
- Dipartimento di Fisica, Universita degli Studi di Padova (Italy) and Istituto Nazionale di Fisica Nucleare, Sezione di Padova, Via F. Marzolo, 8, 35131 Padova (Italy). E-mail: pieralberto.marchetti@pd.infn.it

- Publication Date:

- OSTI Identifier:
- 20976759

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics (New York); Journal Volume: 322; Journal Issue: 5; Other Information: DOI: 10.1016/j.aop.2006.07.002; PII: S0003-4916(06)00136-9; 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:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BRANES; COSMOLOGICAL MODELS; DIRAC EQUATION; ELECTRODYNAMICS; ENERGY-MOMENTUM TENSOR; INTERACTIONS; LORENTZ INVARIANCE; MANY-DIMENSIONAL CALCULATIONS; POINT CHARGE; RELATIVISTIC RANGE; RENORMALIZATION; STRING THEORY; VARIATIONAL METHODS

### Citation Formats

```
Lechner, K., and Marchetti, P.A..
```*Variational principle and energy-momentum tensor for relativistic electrodynamics of point charges*. United States: N. p., 2007.
Web. doi:10.1016/j.aop.2006.07.002.

```
Lechner, K., & Marchetti, P.A..
```*Variational principle and energy-momentum tensor for relativistic electrodynamics of point charges*. United States. doi:10.1016/j.aop.2006.07.002.

```
Lechner, K., and Marchetti, P.A.. Tue .
"Variational principle and energy-momentum tensor for relativistic electrodynamics of point charges". United States.
doi:10.1016/j.aop.2006.07.002.
```

```
@article{osti_20976759,
```

title = {Variational principle and energy-momentum tensor for relativistic electrodynamics of point charges},

author = {Lechner, K. and Marchetti, P.A.},

abstractNote = {We give a new representation as tempered distribution for the energy-momentum tensor of a system of charged point-particles, which is free from divergent self-interactions, manifestly Lorentz-invariant and symmetric, and conserved. We present a covariant action for this system, that gives rise to the known Lorentz-Dirac equations for the particles and entails, via Noether theorem, this energy-momentum tensor. Our action is obtained from the standard action for classical electrodynamics, by means of a new Lorentz-invariant regularization procedure, followed by a renormalization. The method introduced here extends naturally to charged p-branes and arbitrary dimensions.},

doi = {10.1016/j.aop.2006.07.002},

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

number = 5,

volume = 322,

place = {United States},

year = {Tue May 15 00:00:00 EDT 2007},

month = {Tue May 15 00:00:00 EDT 2007}

}

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