Abstract
We make a thorough non-covariant analysis of the derivation of the equation of motion for a charged particle, including radiation reaction, by means of a simple model for the charge: a dumbbell. This model and our method to expand retarded quantities, based on complex-variable theory, allow us to avoid some of the usual approximations, so we can show several features of the radiation reaction problem.
Similar content being viewed by others
References
G. Arfken, 1970,Mathematical Methods for Physicists, 2nd edn. (New York: Academic), pp. 269–270 and 366–367.
A. O. Barut, 1974,Phys. Rev. D 10, 3335–3336.
R. Bellman, 1972,Perturbations Techniques in Mathematics, Engineering and Physics (New York: Dover), pp. 5–7 and 50–51.
D. Bohm and M. Weinstein, 1948,Phys. Rev. 74, 1789–1792.
M. Bunge, 1967,Foundations of Physics (Berlin: Springer), Chap. IV, Sec. 1.
I. Campos and J. L. Jiménez, 1986,Phys. Rev. D 33, 607–610; 1989,Am. J. Phys. 57, 610–613; 1992,Eur. J. Phys. 13, 117–122.
R. Churchill, J. W. Brown, and R. F. Verhey, 1974,Theory of Complex Variable and its Applications (New York: McGraw Hill), pp. 298–301 and p. 302, problem 12.
J. Daboul, 1974,Int. J. Theoret. Phys. 11, 145–147.
L. de la Peña, J. L. Jiménez, and R. Montemayor, 1982,Nuovo Cimento B69, 71–78.
P. A. M. Dirac, 1938,Proc. R. Soc. A 167, 148–169.
Enz, 1973,Pauli Lectures on Physics Vol. 1 (Cambridge: MIT Press), pp. 387–389.
L. Eyges, 1980,the Classical Electromagnetic Field (New York: Dover), pp. 298–300.
H. M. França, G. C. Marques, and A. J. da Silva, 1978,Nuovo Cimento A48, 65–83.
G. H. Goedecke, 1975,Nuovo Cimento B28, 225.
E. Goursat, 1959,A Course in Mathematical Analysis (New York: Dover), pp. 404–406 (Vol. 1) and 106–109 (Vol. 2).
I. S. Gradshteyn and I. M. Ryzhik, 1980,Tables of Integrals, Series and Products (New York: Academic), p. 14.
D. J. Griffiths and E. W. Szeto E. W., 1978,Am. J. Phys. 46, 244–248; 1981,Introduction to Electrodynamics (Englewood Cliffs, New Jersey: Prentice Hall), pp. 380–386. R. E. Owen, 1983,Am. J. Phys. 51, 1120–1126.
A. Grünbaum and A. I. Janis, 1978,Am. J. Phys. 46, 337–341.
W. Heitler, 1984,The Quantum Theory of Radiation, 3rd edn. (New York: Dover), pp. 25–34.
J. D. Jackson, 1975,Classical Electrodynamics, 2nd edn. (New York: Wiley), pp. 657 and 783–791.
J. L. Jiménez and R. Montemayor, 1983a,Nuovo Cimento B73, 246–257; 1983b,Nuovo Cimento B75, 87–104. J. L. Jiménez, R. Blanco, and L. Pesquera, 1985,J. Phys. A18 1173–1192. J. L. Jiménez and I. Campos, 1987,Am. J. Phys. 55, 1017–1023. J. L. Jiménez, 1989,Ciencia 40, 257–274.
E. J. Konopinski, 1981,Electromagnetic Fields and Relativistic Particles (New York: McGraw-Hill), pp. 441–442.
H. A. Lorentz, 1952,The Theory of Electrons 2nd edn. (New York: Dover), pp. 48–49, 252–254.
E. Marx, 1975,Int. J. Theoret. Phys. 14, 55–65.
W. K. H. Panofsky and M. Phillips, 1962,Classical Electricity and Magnetism 2nd edn. (Reading, Massachusetts: Addison-Wesley), pp. 386–390.
M. Planck, 1896,Berliner Berichte 151–170; 1897,Ann. Phys. 60, 577–599.
A. F. Rañada and M. Rañada, 1979,J. Phys. A12, 1419.
F. Rohrlich, 1965,Classical Charged Particles (Reading, Massachusetts: Addison-Wesley), pp. 11–18.
E. G. P. Rowe, 1975,Phys. Rev. D 12 1576–1587.
M. R. Spiegel, 1964,Complex Variables (New York: McGraw Hill), pp. 145 and 159.
C. Teitelboim, 1970,Phys. Rev. D 1, 1572–1582; 1971,Phys. Rev. D 4, 345–347.
D. Teplitz, 1982,Electromagnetism: Paths to Research (New York: Plenum), Chaps. 6 and 7 (written by S. Coleman and P. Pearle, respectively).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Roa-Neri, J.A.E., Jimenez, J.L. An analysis of the radiation reaction in a charged dumbbell. Found Phys Lett 7, 403–417 (1994). https://doi.org/10.1007/BF02189244
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02189244