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Prog. Theor. Phys. Vol. 9 No. 2 (1953) pp. 137-146

On Yukawa's Theory of Non-local Field, II

— The Interaction of Non-local Fields —

Osamu Hara and Haruo Shimazu^*

Institute of Theoretical Physics, Nagoya University
^*Physical Institute, Yokohama National University

(Received December 30, 1952)

Abstract:

The interaction of non-local fields is investigated using the S-matrix formalism given by Yukawa. In §2 the self-energy of a local spinor particle interacting with a non-local scalar field is calculated in the second order approximation of the coupling constant. The result agrees with that obtained from the local theory except for a meaningless constant factor. The result is compared with those of Yennie and of Rayski, and it is pointed out that such an agreement is a direct consequence of the quantization rule adopted by Yukawa. In §3 the general feature of the Yukawa's S-matrix is discussed, and it is shown that it reduces to the ordinary Dyson's S-matrix in the limit when the particle radius tends to zero. The appendix constants a calculation of the vacuum energy of a system composed of two non-local scalar fields mutually interacting.

URL : http://ptp.ipap.jp/link?PTP/9/137/
DOI : 10.1143/PTP.9.137

[ Full Text PDF : FREE ACCESS (771K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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References:

1. O. Hara and H. Shimazu, Prog. Theor. Phys. 5 (1950), 1055[PTP].
2. O. Hara and H. Shimazu, Prog. Theor. Phys. 7 (1952), 255[PTP].
3. H. Yukawa, Phys. Rev. 77 (1950), 219[APS].
4. M. Fierz, Phys. Rev. 78 (1950), 184[APS].
5. H. Yukawa, Phys. Rev. 80 (1950), 1047[APS].
6. D. R. Yennie, Phys. Rev. 80 (1950), 1053[APS].
7. J. Rayski, Proc. R. Soc. A 206 (1951), 575.
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9. S. Sakata, H. Umezawa and S. Kamefuchi, Prog. Theor. Phys. 7 (1952), 377[PTP].
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Citing Article(s) :

1. Progress of Theoretical Physics Vol. 9 No. 5 (1953) pp. 559-560 :

   The Theory of the Structure of Elementary Particles

   Osamu Hara and Toshio Marumori

2. Progress of Theoretical Physics Vol. 12 No. 2 (1954) pp. 177-207 :

   An Attempt to the Unified Description of Elementary Particles

   Osamu Hara, Toshio Marumori, Yoshio Ohnuki and Hajime Shimodaira

3. Progress of Theoretical Physics Vol. 59 No. 3 (1978) pp. 996-1008 :

   S-Matrix for Interacting Extended Boson Field. I

   A. Z. Capri and C. C. Chiang

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