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2013

Finite field-energy of a point charge in QED

Costa, Caio V., Gitman, Dmitri M., Shabad, Anatoly E.

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We consider a simple nonlinear (quartic in the fields) gauge-invariant modification of classical electrodynamics, which possesses a regularizing ability sufficient to make the field energy of a point charge finite.

The model is exactly solved in the class of static central-symmetric electric fields.
Collation with quantum electrodynamics (QED) results in the total field energy about twice the electron mass.
The proof of the finiteness of the field energy is extended to include any polynomial selfinteraction, thereby the one that stems from the truncated expansion of the Euler-Heisenberg local Lagrangian in QED in powers of the field strenth.

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M. Born and L. Infeld, Electromagnetic mass, Nature, 132
1933
Earlier work this paper cites.
G. Boillat, Nonlinear electrodynamics: Lagrangians and equations of motion, J. Math. Phys. 11
1970
Earlier work this paper cites.
V. B. Berestetsky, E. M. Lifshits, and L. P. Pitayevsky, Quantum Electrodynamics (Nauka, Moscow, 1989; Pergamon Press, Oxford, New York, 1982)
1982
Earlier work this paper cites.

Similar

S. Weinberg, The Quantum Theory of Fields (University Press, Cambridge, 2001)
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Lorentz, H.A., Weiterbildung der Maxwell’schen Theorie: Elektronentheorie., Encyklopädie d. Mathematischen Wissenschaften, Band V2, Heft 1, Art. 14, 145-288 (1904); Abraham, M., Theorie der Elektrizität , II , Teubner, Leipzig (1905,1923); Rohrlich, F., Classical charged particles , Addison Wesley, Redwood City, CA (1990); Spohn, H., Dynamics of charged particles and their radiation field , Cambridge University Press, Cambridge (2004)
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A.E. Shabad and V.V. Usov, Effective Lagrangian in nonlinear electrodynamics and its properties of causality and unitarity, Phys. Rev. D 83,
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Then

D. M. Gitman and A. E. Shabad, Nonlinear (magnetic) corrections to the field of a static charge in an external field, Phys. Rev. D 86
Original
2012
Later among the works it cites.
C. V. Costa, D.M. Gitman, and A.E.Shabad, Nonlinear corrections in basic problems of electro- and magneto-statics in the vacuum, Phys. Rev. D 88
Original
2013
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