Advertisement

Communications in Mathematical Physics

, Volume 57, Issue 3, pp 235–258 | Cite as

Strong coupling in the quantum field theory with nonlocal nonpolynomial interaction

  • G. V. Efimov
Article

Abstract

In the relativistic quantum field theory the representation for theS-matrix elements is obtained for any coupling constantsg in the case of a one component scalar field ϕ(x) with nonlocal nonpolynomial interaction ℒ I (ϕ)=gU(ϕ) when the causal function is bounded in the Euclidean region 0≦D c (x E 2 D c (0)<∞ and the function |U(u)|≦1 for realu. It is proved that the two point Green function is bounded in the physical region of momenta variablep2.

Keywords

Neural Network Statistical Physic Field Theory Complex System Quantum Field Theory 
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.
    Alebastrov, V.A., Efimov, G.V.: Commun. math. Phys.31, 1 (1973);38, 11 (1974)Google Scholar
  2. 1.a
    Efimov, G.V.: Nonlocal interactions of quantized fields. Moscow: Nauka 1977Google Scholar
  3. 2.
    Petrina, D.Ja., Skripnik, V.I.: Sovjet Teor. Math. Phys.8, 368 (1971)Google Scholar
  4. 3.
    Basuev, A.G.: Sovjet Teor. Math. Phys.16, 281 (1973)Google Scholar
  5. 4.
    Hardy, G.H., Littlewood, J.E., Polya, G.: Inequalities. London: Cambridge University Press 1951Google Scholar
  6. 5.
    Titchmarsh, E.C.: The theory of functions. London: Oxford University Press 1939Google Scholar
  7. 6.
    Shilov, G.E., Gurevitch, B.L.: Integral, measure and derivative. Moscow: Nauka 1967Google Scholar
  8. 7.
    Szego, G.: Orthogonal polynomials. New York: American Mathematical Society 1959Google Scholar

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • G. V. Efimov
    • 1
  1. 1.Laboratory of Theoretical PhysicsJoint Institute for Nuclear ResearchDubnaUSSR

Personalised recommendations