Theoretical and Mathematical Physics

, Volume 107, Issue 1, pp 487–498 | Cite as

Analogs of Fourier series for a relativistic string model with massive ends

  • G. S. Sharov
Article

Abstract

A description of the motions of a relativistic string with massive ends (for the model with a finite mass on the first end and an infinite mass on the second end) is proposed. This approach uses the expansion of the string world surface into a series that is not reduced to the ordinary Fourier series due to the nonlinearity of the problem. The state equation of the string is derived from the mass shell condition for its end. The string motions are classified, allowing linearization of the boundary condition by a natural parametrization of the trajectory of the moving end. The set of such world surfaces is shown to be limited; for the special cases of 2+1 - and 3+1-dimensional Minkowski spaces, all of them reduce to a helicoid.

Keywords

Boundary Condition Fourier Fourier Series State Equation Minkowski Space 

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References

  1. 1.
    B. M. Barbashov and V. V. Nesterenko,Introduction to the Relativistic String Theory, World Scientific, Singapore (1990).Google Scholar
  2. 2.
    A. Chodos and C. B. Thom,Nucl. Phys.,B72, 509 (1974).Google Scholar
  3. 3.
    B. M. Barbashov and A. M. Cherviakov,Teor. Mat. Fiz.,74, 430 (1988);89, 105 (1991).Google Scholar
  4. 4.
    B. M. Barbashov,Nucl. Phys.,B129, 175 (1977).Google Scholar
  5. 5.
    B. M. Barbashov and G. S. Sharov,Teor. Mat. Fiz.,101, 253 (1994).Google Scholar
  6. 6.
    B. M. Barbashov, “Classical dynamics of a rotating relativistic string with massive ends: the Regge trajectories and quark masses.” Preprint E2-94-444, Joint Inst. Nucl. Res., Dubna (1994).Google Scholar
  7. 7.
    A. Yu. Morozov.Usp. Fiz. Nauk. 162, 83 (1992).Google Scholar
  8. 8.
    M. Green, J. Schwarz, and E. Witten,Superstring Theory, Vol. 1, Cambridge University Press, Cambridge (1987).Google Scholar
  9. 9.
    G. S. Sharov,Teor. Mat. Fiz.,102, 150 (1995).Google Scholar
  10. 10.
    B. M. Barbashov and V. V. Nesterenko,Teor. Mat. Fiz.,31, 291 (1977).Google Scholar
  11. 11.
    V. A. Steklov,The Basic Problems of Mathematical Physics [in Russian], Nauka, Moscow (1983).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • G. S. Sharov
    • 1
  1. 1.Tver' State UniversityUSSR

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