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On a convergent non-local field theory. — I.

  • Published:1960-05 Issue:4 Volume:16 Page:671-682
  • ISSN:0029-6341
  • Container-title:Il Nuovo Cimento
  • language:en
  • Short-container-title:Nuovo Cim

Author:

Arnous E.,Heitler W.,Takahashi Y.

Publisher

Springer Science and Business Media LLC

Subject

Astronomy and Astrophysics,Nuclear and High Energy Physics,Atomic and Molecular Physics, and Optics

Reference7 articles.

1. Compare for instance:Ch. Møller andP. Kristensen:Kgl. Dan. Vid. Selsk.,27, no. 7 (1952);

2. C. Bloch:Kgl. Dan. Vid. Selsk.,27, no. 8 (1952);

3. G. Wataghin:Nuovo Cimento,5, 689 (1957), and numerous other papers.

4. The following facts can be quoted in this connexion: (i) the π±-π0 mass difference which is probably mainly an electromagnetic self-energy; (ii) the proton-neutron mass difference which is probably a mixed electromagnetic-mesonic self-energy, ordere 2 f 2,e 2 f 4 … (cfr.R. P. Feynmann andG. Speismann:Phys, Rev.,94, 500 (1954), andL. O’Raifeartaigh, B. Sredniawa andCh. Terreaux:Nuovo Cimento,14, 376 (1959)). Perhaps similar considerations obtain for the K0-K+ mass difference. (iii) The π-nucleon scattering. While perturbation theory based on the first order gave on the whole the correct gross behaviour of the cross section (W. Heitler andH. W. Peng:Proc. Cam. Phil. Soc.,38, 296 (1942)), the quantitative improvement (G. F. Chew:Phys. Rev.,94, 1748, 1755 (1954)), due to the inclusion of higher orders on grounds of the non-relativistic extended source model is very considerable. The same applies to the photo-meson production. It may be remarked that in these calculations thenon-renormalizable p.v. coupling is used which, forsecond order processes is not the non-relativistic limit of the p.s. coupling (contrary to numerous statements made in the literature). Thus the use of a finite size model is imperative. (iv) Although the finite size of the charge and of the magnetic moment distribution of the nucleons is primarily an effect of meson theory (compareM. Slotnick andW. Heitler:Phys. Rev.,75, 1645 (1949)) a quantitative investigation indicates a finite size of the nucleon itself. (L. K. Pandit:Helv. Phys. Acta,31, 379 (1958);Nuovo Cimento,10, 534 (1958)). All these effects lead to a size of the elementary particles of the orderħ/Mc,M = nucleon mass, for all interactions.

5. E. Arnous andW. Heitler:Nuovo Cimento,11, 443 (1959), cfr. also Part II, Sect.6. In the first paper theC, P. T invariance and causality are also discussed.

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