Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-14T22:19:15.070Z Has data issue: false hasContentIssue false
  • English
  • Français

X.—The Reciprocity Theory of Electrodynamics*

Published online by Cambridge University Press:  14 February 2012

H. S. Green  and
K. C. Cheng
H. S. Green
Affiliation:
University of Edinburgh
K. C. Cheng
Affiliation:
University of Edinburgh
Get access Rights & Permissions [Opens in a new window]

Synopsis

This paper represents the application of the Principle of Reciprocity, formulated in a previous communication, to the outstanding problems of classical and quantum electrodynamics.

The first step consists in the formulation of a reciprocally invariant Lagrangian function for a system of electrons in interaction with the electromagnetic field. A study is made of the unaccelerated motion of an electron, and this is subsequently extended to embrace the problem of an electron in arbitrary motion. It is found that the usual difficulties of classical electrodynamics do not appear. The methods of the earlier paper are applied to the derivation of the Hamiltonian energy of electron and field, and this enables a quantized formulation of the theory to be given, which also does not lead to the usual divergence difficulties.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 63 , Issue 2 , 1951 , pp. 105 - 138
Copyright
Copyright © Royal Society of Edinburgh 1951

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

References to Literature

Bopp, F., 1940. Ann. d. Phys., XXXVIII, 345.CrossRefGoogle Scholar
Bopp, F., 1943. Ann. d. Phys., XLII, 575.Google Scholar
Born, M., 1909. Ann. d. Phys., xxx, 1.CrossRefGoogle Scholar
Born, M., 1934. Proc. Roy. Soc., A, CXLIII, 410.Google Scholar
Born, M., 1939. Proc. Roy. Soc. Edin., A, LIX, 219.Google Scholar
Born, M., and Green, H. S., 1949. Proc. Roy. Soc. Edin., A, LXII, 470.Google Scholar
Born, M., and Infeld, L., 1934. Proc. Roy. Soc., A, CXLIV, 425.Google Scholar
Born, M., and Rumer, G., 1931. Zeits.f. Phys., LXIX, 141.CrossRefGoogle Scholar
Dirac, P. A. M., 1938. Proc. Roy. Soc., A, CLXVII, 148.Google Scholar
Dirac, P. A. M., 1942. Proc. Roy. Soc. CLXXX, 1.Google Scholar
Heitler, W., 1944. The Quantum Theory of Radiation, Oxford University Press.Google Scholar
Heitler, W., and Peng, H. W., 1942. Proc. Camb. Phil. Soc., XXXVIII, 296.CrossRefGoogle Scholar
Herglotz, G., 1903. Nach. K. Ges. Wiss. (Göttingen), 357.Google Scholar
Krazer, A., 1904. Verh. des 3. Internationalen Math.-Kongresses (Heidelberg).Google Scholar
McManus, H., 1948. Proc. Roy. Soc., A, CLXXXXV, 323.Google Scholar
Pais, A., 1948. Developments in the Theory of the Electron, Publication of Princeton Institute for Advanced Studies.Google Scholar
Podolsky, B., 1942. Phys. Rev., LXII, 68.CrossRefGoogle Scholar
Pryce, M. H. L., 1938. Proc Roy. Soc., A, CLXVIII, 389.Google Scholar
Schwinger, J., 1948. Phys. Rev., LXXIII, 416.CrossRefGoogle Scholar
Schwinger, J., 1949. Phys. Rev., LXXV, 651.CrossRefGoogle Scholar
Sommerfeld, A., 1904. Nach. K. Ges. Wiss. (Göttingen).Google Scholar
Weisskopf, V., 1934. Zeits. f. Phys., LXXXIX, 27.CrossRefGoogle Scholar