Nonlinear Electrodynamics and QED

Abstract

The limits of linear electrodynamics are reviewed, and possible directions of nonlinear extension are explored. The central theme is that the qualitative character of the empirical successes of quantum electrodynamics must be used as a guide for understanding the nature of the nonlinearity of electrodynamics at the subatomic level. Some established theories of nonlinear electrodynamics, namely, those of Mie, Born, and Infeld are presented in the language of the modern geometrical and topological methods of mathematical physics. The manner by which spacetime curvature and topology can affect electromagnetism is also reviewed. Finally, the phenomena of nonlinear optics are discussed as a possible guide to building one's intuition regarding the process of extending electrodynamics into nonlinearity in a manner that is consistent with the qualitative and empirical results of quantum electrodynamics.

78 pages, 18 figures

References in corpus (3)

• Geometrical aspects of light propagation in nonlinear electrodynamics
• Spacetime G-structures I: Topological Defects
• The Geometric Origin of the Madelung Potential

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• Recent developments in premetric classical electrodynamics
• Self-Interacting Electromagnetic Fields and a Classical Discussion on the Stability of the Electric Charge
• Electromagnetic field objects in terms of Balance of Geometric flows
• A nonlinear prerelativistic approach to mathematical representation of vacuum electromagnetism
• On the Pre-metric Formulation and Nonlinearization of Charge-free Electrodynamics