Abstract
I would like to describe some calculationstl(1,2) which E. J. Moniz and I carried out for the purpose of understanding more clearly the relationship between classical and quantum electrodynamics, particularly in regard to their treatment of radiation reaction. Let us begin by reviewing some of the questions of interest here.
Work supported by the U.S. Department of Energy.
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References and Notes
I. E. J. Moniz and D. H. Sharp, Phys. Rev. D 10, 1133 (1974).
E. J. Moniz and D. H. Sharp, Phys. Rev. D 15, 2850 (1977).
H. A. Lorentz, Theory of Electrons, 2nd ed., Dover, New York (1952).
P. A. M. Dirac, Proc. R. Soc. London Ser. A 167, 148 (1938).
Excellent expositions of the Abraham-Lorentz-Dirac theory can be found in T. Erber, Fortschr. Phys. 9, 343 (1961); J. D. Jackson, Classical Electrodynamics,Wiley, New York (1962)
F. Rohrlich, Classical Charged Particles-Foundations of Their Theory, Addison-Wesley, Reading, Massachusetts (1965).
See the textbook of J. D. Jackson, Reference 5, for details.
The spherical shell has recently been discussed in References 2 and 8. For references to previous work on the motion of classical extended charges, see Reference 2 and the review article of T. Erber, Reference 5.
H. Levine, E. J. Moniz, and D. H. Sharp, Am. J. Phys. 45, 75 (1977).
W. Pauli and M. Fierz, Nuovo Cimento 15, 157 (1938).
In obtaining the equation of motion we introduce a static charge distribution p into the Hamiltonian. We will pass to the point limit at a later stage of the calculation.
We have checked that our calculation leads to the same results if one works in Coulomb gauge.
The only properties of the Hamiltonian that are used to carry out the evaluation are that aj(r, t)/at = i[H,j(r, t)] and that aplat = i[H, p] _ — V j, with the current density given by j(r, t) = l[p(r — R(t)), R(t)]+.
V. F. Weiskopf, Phys. Rev. 56, 72 (1939).
This point has also been emphasized recently by F. Rohrlich, Acta Phys. Austriaca 41, 375 (1975).
H. Grotch and E. Kazes, Phys. Rev. D 16, 3605 (1977).
H. Grotch, E. Kazes, F. Rohrlich, and D. H. Sharp, in preparation.
F. Rohrlich, Chapter 13 of this volume.
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Sharp, D.H. (1980). Radiation Reaction in Nonrelativistic Quantum Theory. In: Barut, A.O. (eds) Foundations of Radiation Theory and Quantum Electrodynamics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0671-0_10
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