Advertisement

Antibrackets and Supersymmetric Mechanics

  • Armen Nersessian
Part of the NATO ASI Series book series (NSSB, volume 331)

Abstract

Using the odd symplectic structure constructed over the tangent bundle of the symplectic manifold we construct the simple supergeneralization of an arbitrary Hamiltonian mechanics. In the case where the initial mechanics defines the Killing vector of some Riemannian metric, the corresponding supersymmetric mechanics can be reformulated in terms of the even symplectic structure on the supermanifold.

Keywords

Hamiltonian System Poisson Bracket Tangent Bundle Symplectic Manifold Symplectic Structure 
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.
    F. A. Berezin — Introduction to Superanalysis., D. Reidel, Dordrecht, 1986.Google Scholar
  2. T. Voronov — Geometric Integration Theory on Supermanifolds. Sov. Sci. Rev. C, Math.Phys., 9 (1992), 1.Google Scholar
  3. 2.
    D. A. Leites — Dokl. Akad. Nauk SSSR, 236(1977), 804.MathSciNetGoogle Scholar
  4. 3.
    V. N. Shander — Dokl. Akad. Nauk. Bulgaria 36 (1983), 309.zbMATHMathSciNetGoogle Scholar
  5. 4.
    I. A. Batalin, G. A. Vilkovisky — Phys.Lett., 102B(1981), 27.ADSCrossRefMathSciNetGoogle Scholar
  6. I.
    A. Batalin, G. A. Vilkovisky — Phys. Rev., D28(1983), 2567.ADSMathSciNetGoogle Scholar
  7. 5.
    I. A. Batalin, P. M. Lavrov, I. V. Tyutin — J. Math. Phys., 31(1990) 1487.ADSCrossRefzbMATHMathSciNetGoogle Scholar
  8. I.
    A. Batalin, P. M. Lavrov, I. V. Tyutin — J. Math. Phys., 32(1991), 532.ADSCrossRefzbMATHMathSciNetGoogle Scholar
  9. I.
    A. Batalin, P. M. Lavrov, I. V. Tyutin — J. Math. Phys., 32(1991), 2513.ADSCrossRefMathSciNetGoogle Scholar
  10. I.
    A. Batalin, I. V. Tyutin — Int. J. Mod. Phys., A8 (1993) 2333.ADSCrossRefMathSciNetGoogle Scholar
  11. 6.
    E. Witten — Mod. Phys. Lett., A5 (1990), 487; Phys. Rev., D46(1992), 5446.ADSCrossRefMathSciNetGoogle Scholar
  12. 7.
    D. V. Volkov — JETP Lett., 38(1983), 508.Google Scholar
  13. D. V. Volkov, V. A. Soroka, V. I. Tkach — Sov. J. Nucl. Phys., 46 (1987), 110.Google Scholar
  14. 8.
    D. V. Volkov, V. A. Soroka, A. I. Pashnev, V. I. Tkach — JETP Lett., 44 (1986), 55.Google Scholar
  15. 9.
    O. M. Khudaverdian, A. P. Nersessian — Preprint YERPHI-1031(81)-1987; J. Math. Phys, 32 (1991), 1938; J. Math. Phys, 34 (1993), No. 11 (to appear).Google Scholar
  16. O. M. Khudaverdian — J. Math. Phys, 32(1991), 1934.ADSCrossRefzbMATHMathSciNetGoogle Scholar
  17. A. P. Nersessian — Theor. Math. Phys., 96 (1993), 140.MathSciNetGoogle Scholar
  18. 10.
    M. Blau, E. Keski-Vakkuri, A. J. Niemi — Phys.Lett., B246(1990), 92.ADSCrossRefMathSciNetGoogle Scholar
  19. A. Hietamaki, A. Yu. Morozov, A. J. Niemi, K. Palo — Phys. Lett. B263(1991), 417.ADSCrossRefMathSciNetGoogle Scholar
  20. A. Yu. Morozov, A. J. Niemi, K. Palo — Nucl. Phys. B377(1992), 295; E. Witten — Preprint IASSNS-HEP-92/15.ADSCrossRefMathSciNetGoogle Scholar
  21. 11.
    A. J. Niemi, O. Tirkkonen — Preprint UU-ITP 3/93.Google Scholar
  22. 12.
    J. J. Duistermaat, G. J. Heckman — Inv. Math. 69 (1982), 259.ADSCrossRefzbMATHMathSciNetGoogle Scholar
  23. J. J. Duistermaat, G. J. Heckman — Inv. Math. 72(1983), 153.ADSCrossRefzbMATHMathSciNetGoogle Scholar
  24. M. F. Atiah, R. Bott — Topology, 23, No. 1 (1984), 1.CrossRefMathSciNetGoogle Scholar
  25. 13.
    A.P. Nersessian — JETP Lett., 58 (1993), 64.ADSMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Armen Nersessian
    • 1
  1. 1.Laboratory of Theoretical PhysicsJINR, DubnaMoscowRussia

Personalised recommendations