Letters in Mathematical Physics

, Volume 16, Issue 1, pp 61–67 | Cite as

Harmonic analysis and p-adic strings

  • I. V. Volovich


A generalization of the Veneziano amplitude is considered which is a convolution of two characters on a field K. Choosing K in an appropriate way, one can obtain the usual Veneziano amplitude, the Virasoro-Shapiro amplitude, the p-adic amplitudes, and the finite Galois field amplitude. The cases when K is an algebra or a group are also discussed. These cases can be of interest in the context of the quantization of spacetime.


Statistical Physic Convolution Harmonic Analysis Group Theory Field Amplitude 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    VolovichI. V., Theor. Math. Fiz. 71, 337 (1987).Google Scholar
  2. 2.
    Volovich I. V., Class. Quan. Grav. 4, L83 (1987).Google Scholar
  3. 3.
    VladimirovV. S. and VolovichI. V., Theor. Math. Fiz. 59, 3 (1984).Google Scholar
  4. 4.
    Volovich, I. V., Preprint, CERN-TH.4781/87.Google Scholar
  5. 5.
    HewittE. and RossK. A., Abstract Harmonic Analysis, Vols. I and II, Springer-Verlag, New York, 1963.Google Scholar
  6. 6.
    Gelfand, I. M., Graev, M. I., and Pjatetskii-Shapiro, I. I., Representation Theory and Automorphic Functions, Saunders, 1966.Google Scholar
  7. 7.
    VenezianoG., Phys. Rep. 9C, 199 (1974); Schwarz, J. H., Phys. Rep. 89C, 223 (1982).Google Scholar
  8. 8.
    Freund, P. G. O. and Olson, M., Chicago preprint EF187-54.Google Scholar
  9. 9.
    Arefeva, I. Ya., Lectures delivered at Potana Brasov School, 1987 (to be published by Academic Press); Horowitz, G. T., Lectures delivered at the ICTP School on Superstring, 1987. Preprint UCSBTH-87-38.Google Scholar
  10. 10.
    MarkovM. A., JETF, 10, 1311 (1940); 21, 11 (1951). Snyder, H. S., Phys. Rev. 71, 38 (1947); Yang, C. N., Phys. Rev. 72, 874 (1947); Yukawa, H., Phys. Rev. 91, 415 (1953); Finkelstein, D., Phys. Rev. 184, 1261 (1969).Google Scholar
  11. 11.
    Pontryagin, L. S., Topological Groups, Gordon and Breach, 1966.Google Scholar
  12. 12.
    Hofmann, K. H., Lecture Notes in Math. 129 (1970); Bergman, G. M., Contemp. Math. 43, 25 (1985).Google Scholar
  13. 13.
    SweedlerM. E., Ann. Math. 89, 323 (1969).Google Scholar
  14. 14.
    Doplicher, S. and Roberts, J. E., J. Funct. Anal. (1987); Horuzhy, S. S., Introduction to Algebraic Quantum Field Theory, Kluwer Academic Publishers, Dordrecht, 1988, in press.Google Scholar
  15. 15.
    Arefeva, I. Ya., Dragovic, B. G., and Volovich, I. V., Preprint Belgrade, IF-12/87.Google Scholar
  16. 16.
    Grossmann, B., Rockefeller University preprint (1987).Google Scholar
  17. 17.
    Freund, P. G. O. and Witten, E., Preprint IASSNS-HEP-87/42.Google Scholar
  18. 18.
    Arfeva, I. Ya, Dragović, B., and Volovich, I. V., On the Adelic string amplitudes, Preprint IF-13/88, Belgrade (1988).Google Scholar

Copyright information

© Kluwer Academic Publishers 1988

Authors and Affiliations

  • I. V. Volovich
    • 1
  1. 1.Steklov Mathematical InstituteMoscowUSSR

Personalised recommendations