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Il Nuovo Cimento A (1965-1970)

, Volume 89, Issue 2, pp 204–215 | Cite as

The electromagnetic field in classical space-time

  • N. Kadianakis
Article

Summary

We give a frame-independent representation of the electromagnetic field on classical, nonrelativistic, space-time in terms of an affine connection of it (or even a 2-form in some cases). Maxwell's equations are thus expressed as properties of the Riemann curvature tensor of this connection. Although this representation does not have the covariant character of the relativistic electromagnetism, it shows the may of associating dynamical systems with affine connections. In this context the equation of motion is associated with the geodesic equation of the connection.

PACS. 11.10

Field theory 

PACS. 04.90

Other topics in relativity and gravitation 

PACS. 02.40

Geometry differential geometry and topology 

Riassunto

Si propone una rappresentazione indipendente dal sistema del campo elettromagnetico sullo spazio-tempo classico, non relativistico in termini di una connessione affine su questo (o anche una 2-forma in alcuni casi). Le quazioni di Maxwell sono cosí espresse come proprietà dei tensore di curvatura di Riemann di questa connessione. Sebbene questa rappresentazione non abbia il carattere covariante dell'elettromagnetismo relativistico, si mostra il modo di associare sistami dinamici con connessioni affini. In questo contesto si associa l'equazione di moto all'equazione geodesica di connessione.

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Copyright information

© Società Italiana di Fisica 1985

Authors and Affiliations

  • N. Kadianakis
    • 1
  1. 1.Department of MathematicsNational Technical UniversityAthensGreece

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