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All nonlinear extensions of the source-free Maxwell equations preserving both SO(2) electromagnetic duality invariance and conformal invariance are found, and shown to be limits of a one-parameter generalisation of Born-Infeld electrodynamics.
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M. Born and L. Infeld, “Foundations of the new field theory,” Proc. Roy. Soc. Lond. A A144
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W. Heisenberg and H. Euler, “Consequences of Dirac’s theory of positrons,” Z. Phys. 98
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J. Plebanski, “Lectures on nonlinear electrodynamics”, (Nordita, Copenhagen, 1970)
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I. Bialynicki-Birula, “Nonlinear Electrodynamics: Variations on a theme by Born and Infeld”, in Quantum Theory Of Particles and Fields: birthday volume dedicated to Jan Łopuszański
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I. Bialynicki-Birula, “Field theory of photon dust,” Acta Phys. Polon. B 23
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G. W. Gibbons, “Aspects of Born-Infeld theory and string/M theory,” AIP Conf. Proc. 589
2001
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2005
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B. Kosyakov, “Introduction to the classical theory of particles and fields,” (Springer, 2007)
2007
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2017
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