Advertisement

Communications in Mathematical Physics

, Volume 40, Issue 3, pp 259–272 | Cite as

Descending problem in Green's function approach to quantum field theory

  • Tetz Yoshimura
Article

Abstract

The question how to determine lower many-point functions in terms of higher ones, which we call the descending problem, is discussed for the (ø4)1+3 model of quantum field theory. Equations to be considered are non-linear non-compact operator equations in complex Banach spaces.

Several sufficient sets of conditions for convergence of successive approximation schemes are presented for small values of the renormalised coupling constant. Local uniqueness of solution is proved under certain conditions.

Keywords

Neural Network Statistical Physic Banach Space Field Theory Complex System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Taylor, J.G.: Lectures in Theoretical Physics, X, pp. 221–268. Boulder, Colorado, 1968Google Scholar
  2. 2.
    Landau, L.D., Abrikosov, A.A., Khalatnikov, I.M.: DAN SSSR94, 497–500, 773–776, 1197–1200 (1954)Google Scholar
  3. 3.
    Elworthy, K.D., Tromba, A.J.: Proc. Symp. Pure Math. Amer. Math. Soc.15, 45–94 (1969)Google Scholar
  4. 4.
    Earle, C.J., Hamilton, R.S.: Proc. of Symp. Pure Math. Amer. Math. Soc.16, 61–65 (1970)Google Scholar
  5. 5.
    Petryshyn, W.V.: Proc. Symp. Pure Math. Amer. Math. Soc.18, Part 1, 206–233 (1970)Google Scholar
  6. 6.
    Schiop, A.I.: Metode aproximative în analiza neliniara. Bucureşti: Editura Academiei RSR 1972Google Scholar
  7. 7.
    Jankó, B.: Rezolvarea ecuaţiilor operaţionale neliniare în spaţii Banach. Bucureşti: Editura Academiei RSR 1968Google Scholar
  8. 8.
    Vainberg, M.M.: Variational Methods for the Study of Non-linear Operators. San Francisco: Holden-Day 1964Google Scholar
  9. 9.
    Altman, M.: Contractor with Non-linear Majorant Functions and Equations in Banach Space, Louisiana State University Preprint (1973)Google Scholar
  10. 10.
    Collatz, L.: Arch. Rational Mech. Anal.2, 66–75 (1958)Google Scholar
  11. 11.
    Mirakov, V.E.: Tr. Mosk. Fiz. Tekhn. Inst.1, 204–213 (1958)Google Scholar
  12. 12.
    Jankó, B.: Stud. şi Cerc. Mat.12, 301–308 (1961)Google Scholar
  13. 13.
    Jankó, B.: Stud. şi Cerc. Mat.14, 265–271 (1963)Google Scholar
  14. 14.
    Jankó, B., Balazs, M.: Stud. şi Cerc. Mat.18, 817–828 (1966)Google Scholar
  15. 15.
    Balazs, M., Jankó, B.: Stud. şi Cerc. Mat20, 809–817 (1968)Google Scholar
  16. 16.
    Taylor, J.G., Yoshimura, T.: Which Green's Functions Equations? King's College (London) Preprint (1973)Google Scholar
  17. 17.
    Maris, Th.D., Herscovitz, V.E., Jacob, G.: Phys. Rev. Letters12, 313–315 (1964)Google Scholar
  18. 18.
    Pagels, H.: Phys. Rev. D7, 2689–2698 (1973)Google Scholar
  19. 19.
    Krasnosel'skii, M.A., Vainikko, G.M., Zabreiko, P.P., Ruttiskii, Ya.B., Stetsenko, V.Ya.: Priblizhennoe reshenie operatornykh uravenenii, Moskva Izd. “Nauka” (1969), and earlier works cited thereinGoogle Scholar

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • Tetz Yoshimura
    • 1
  1. 1.Department of MathematicsKing's CollegeLondonEngland

Personalised recommendations