Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-24T17:10:14.407Z Has data issue: false hasContentIssue false

A note on Riesz potential

Published online by Cambridge University Press:  24 October 2008

F. C. Auluck
Affiliation:
University of DelhiDelhiIndia
L. S. Kothari
Affiliation:
University of DelhiDelhiIndia

Extract

The object of the present paper is to discuss the Fourier expansion of the Riesz potential. For this purpose a new definition of the electromagnetic potentials, depending upon an arbitrary parameter α is given. It is shown that this definition is a generalization of the Wentzel potentials in the α-plane, whereas that given by Fremberg (3) is a generalization of the Maxwell potentials. The analysis is applied to the problem of eliminating, in a straightforward way, the longitudinal part of the potential describing the electromagnetic field. The problem of the quantization of the field, based on its Fourier expansion, will be considered in another paper. The recent work of Tomonaga, Schwinger and Dyson, and the regularization process of Pauli has lifted the theory of quantum electrodynamics to a much higher level of rigour and fruitful applicability. All the same, a further study of Riesz potential seems to us of some interest in this field.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 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

(1)Auluck, F. C. & Kothari, D. S.Proc. Roy. Soc. A, 198 (1949), 170.Google Scholar
(2)Dirac, P. A. M.Quantum electrodynamics. The Dublin Institute for Advanced Studies, Series A, no. 1 (1943), 18.Google Scholar
(3)Fremberg, N. F.Proc. Roy. Soc. A, 188 (1946), 18.Google Scholar
(4)Ma, S. T.Phys. Rev. 71 (1947), 787.CrossRefGoogle Scholar
(5)Watson, G. N.Theory of Bessel functions (Cambridge, 1944).Google Scholar