Science in China Series A: Mathematics

, Volume 51, Issue 4, pp 754–764 | Cite as

The equation of the p-adic closed strings for the scalar tachyon field

  • Vasilii Sergeevich Vladimirov


We investigate the structure of solutions of boundary value problems for a non-linear pseudodifferential equation describing the dynamics (rolling) of p-adic closed strings for a scalar tachyon field.


string tachyon 


46S10 81-02 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Brekke L, Freund P G O. p-Adic numbers in physics. Phys Rep, 233(1): 1–66 (1993)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Moeller N, Schnabl M. Tachyon condensation in open-closed p-adic string theory. J High Energy Phys, 1(11): 1–18 (2004)MathSciNetGoogle Scholar
  3. 3.
    Vladimirov V S. On non-linear equations of p-adic open, closed and open-closed strins (in Russian). Theor Math Phis, 149(3): 354–367 (2006)Google Scholar
  4. 4.
    Frampton P H, Okada Y. Effective scalar field theory of p-adic string. Phys Rev, D37(10): 3077–3079 (1989)MathSciNetGoogle Scholar
  5. 5.
    Green M B, Schwarz J H, Witten E. Superstring Theory T 1,2. Cambridge: Cambridge University Press, 1987Google Scholar
  6. 6.
    Witten E. Noncommutative geometry and string field theory. Nucl Phys, B268: 253 (1986)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Vladimirov V S, Volovich I V, Zelenov E I. p-Adic Analsis and Mathematical Physics. Singapore: World Scientific, 1994Google Scholar
  8. 8.
    Volovich IV. p-adic string. Classical Quantum Gravity, 4: 83–87 (1987)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Brekke L, Freund P G O, Olson M, et al. Non-archimedian string dynamics. Nucl Phys, 302: 365 (1988)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Aref’eva I Y, Joukovskaja L V, Koshelev A S. Time evolution in superstring field theory on non-BPS brane I rolling tachyon and energy-momentum conservation. J High Energy Phys, 9: 12 (2003) ArXiv:hepth/0301137CrossRefGoogle Scholar
  11. 11.
    Vladimirov V S, Volovich Y I. Nonlinear Dynamics Equation in p-adic String Theory. Theor Math Phys, 138(3): 355–368 (2004); ArXiv:math-ph/0306018CrossRefMathSciNetGoogle Scholar
  12. 12.
    Vladimirov V S. The equation of the p-adic open string for the scalar tachion field. Izvestiya: Mathematics 69(3): 487–512 (2005); ArXiv:math-ph/0507018Google Scholar
  13. 13.
    Moeller N, Zwiebach B. Dynamics with Infinitely Many Time Derivatives and Rolling Tachyons. J High Energy Phys, 10: 34 (2002); ArXiv:hep-th/0207107CrossRefMathSciNetGoogle Scholar
  14. 14.
    Sen A. Rolling tachyon. J High Energy Phys, 4: 48 (2002); ArXiv:hep-th/0203211CrossRefGoogle Scholar
  15. 15.
    Ghoshal D, Sen A. Tachyon condensation and Brane descent relations in p-Adic string theory. Nucl Phys, 584: 300–312 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Barnaby N. Caustic formation in Tachyon effective field theories. ArXiv:hep-th/0406120Google Scholar
  17. 17.
    Coletti E, Sigalov I, Taylor W. Taming the Tachion in Cubic String Field Theory. J High Energy Phys, 8:104 (2005); ArXiv:hep-th/0505031CrossRefMathSciNetGoogle Scholar
  18. 18.
    Vladimirov V S. On the non-linear equation of a p-adic open string for the scalar field. Russian Math Surveys, 60(6): 1077–1092 (2005)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Aref’eva I Y. Nonlocal string Tachyon as a model for coomological dark engrgy. In: Conf Proc, Vol. 826, 2006, 301–311; ArXiv:astro-ph10410443CrossRefMathSciNetGoogle Scholar
  20. 20.
    Calcagni G. Cosmological tachyon from cubic string field theory. J High Energy Phys, 5: 12 (2006); ArXiv:hep-th/0512259CrossRefMathSciNetGoogle Scholar
  21. 21.
    Lieb E H, Loss M. Analysis. In: Graduate Studies in Mathematics, Vol. 14, Provindence, RI: AMS, 2001Google Scholar
  22. 22.
    Vladimirov V S. Methods of the Theory of Generalized Functions. London-New York: Taylor and Francis, 2002zbMATHGoogle Scholar
  23. 23.
    Wiener N. The Fourier Integral and Certain of its Applications. New York: Dover Publications, 1933Google Scholar

Copyright information

© Science Press 2008

Authors and Affiliations

  1. 1.Steklov Mathematical Institute Russion of SciencesMoscowRussia

Personalised recommendations