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Peeling and conservation laws in the Born-Infeld theory of electromagnetism

Published online by Cambridge University Press:  24 October 2008

John R. Porter
John R. Porter
Affiliation:
Department of Mathematics, University of Pittsburgh
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Extract

1. Introduction Born and Infeld originally proposed their non-linear theory of electromagnetism (1) as one derivable from a Lorentz invariant Lagrangian and, in contradistinction to the usual Maxwell theory, possessing solutions of the ‘point charge’ type without singularities at the position of the charge. Subsequently, examination of the theory by means of iterative methods (2) has demonstrated the self-scattering of outgoing radiation and the existence of wave tails. In the present paper it is shown that the theory, under suitable asymptotic conditions, gives rise to peeling of the type exhibited by Maxwell's theory as well as by the asymptotically flat space-times of general relativity (3, 4, 5). It is also shown that certain conserved quantities exist paralleling those exhibited in the above theories. The Maxwell theory exhibits a sequence of such conserved quantities, the truncation of which is examined in detail for the Born-Infeld theory.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 72 , Issue 2 , September 1972 , pp. 319 - 324
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

REFERENCES

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