Theoretical and Mathematical Physics

, Volume 97, Issue 2, pp 1259–1266 | Cite as

Hierarchical Dyson model andp-adic conformal invariance

  • É. Yu. Lerner
Article
  • 34 Downloads

Abstract

The condition of conformal invariance of a field of ap-adic argument is reformulated in terms of the hierarchical Dyson model. A non-Gaussian scale-invariant random field of ap-adic argument (ϕ d 4 theory with propagator |x-y|d/2+ε) is rigorously constructed, and its conformal invariance is proved.

Keywords

Random Field Conformal Invariance Dyson Model 

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References

  1. 1.
    I. V. Volovich,Teor. Mat. Fiz.,71, 337 (1987).Google Scholar
  2. 2.
    B. Grossman,Phys. Lett. B,197, 101 (1987).Google Scholar
  3. 3.
    P. G. Freund and M. Olson,Phys. Lett. B,199, 186 (1987).Google Scholar
  4. 4.
    P. G. Freund and E. Witten,Phys. Lett. B,199, 191 (1987).Google Scholar
  5. 5.
    V. S. Vladimirov and I. V. Volovich,Dokl. Akad. Nauk SSSR,302, 320 (1988).Google Scholar
  6. 6.
    P. Frampton and Y. Okada,Phys. Rev. Lett.,60, 484 (1988).Google Scholar
  7. 7.
    J. L. Gervais,Phys. Lett. B,201, 306 (1988).Google Scholar
  8. 8.
    É. Yu. Lerner and M. D. Missarov,Teor. Mat. Fiz.,78, 248 (1989).Google Scholar
  9. 9.
    E. Yu. Lerner and M. D. Missarov,Commun. Math. Phys.,121, 35 (1989).Google Scholar
  10. 10.
    A. V. Zabrodin,Commun. Math. Phys.,123, 465 (1989).Google Scholar
  11. 11.
    E. Melzer,Int. J. Mod. Phys. A,4, 4877 (1989).Google Scholar
  12. 12.
    M. D. Missarov,Adv. Sov. Math.,3, 143 (1991).Google Scholar
  13. 13.
    E. Yu. Lerner and M. D. Missarov,Lett. Math. Phys.,22, 123 (1991).Google Scholar
  14. 14.
    V. S. Vladimirov and I. V. Volovich,Tr. Mosk. Inst. Akad. Nauk SSSR,200, 84 (1991).Google Scholar
  15. 15.
    K. Gavedski and A. Kupiainen,Commun. Math. Phys.,99, 197 (1985).Google Scholar
  16. 16.
    T. C. Dorlas, “On some aspects of renormalization group theory and hierarchical models,” Thesis: University of Groningen (1987).Google Scholar
  17. 17.
    N. Koblitz,P-adic Numbers, p-adic Analysis, and Zeta-Functions, New York (1977).Google Scholar
  18. 18.
    Yu. I. Manin, “p-Adic automorphic functions,” in:Reviews of Science and Technology, Modern Problems of Mathematics, Vol. 3 [in Russian], VINITI, Moscow (1974), p. 138.Google Scholar
  19. 19.
    P. M. Bleher and M. D. Misarov,Commun. Math. Phys.,74, 255 (1980).Google Scholar
  20. 20.
    P. M. Bleher and Ya. G. Sinai,Commun. Math. Phys.,33, 23 (1973).Google Scholar
  21. 21.
    P. Collet and J.-P. Eckmann,A Renormalization Group Analysis of the Hierarchical Model in Statistical Mechanics, Lecture Notes in Physics, Vol. 74, Springer-Verlag, Berlin (1978).Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

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  • É. Yu. Lerner

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