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On the geometry of supermanifolds with even and odd Kählerian structures

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Abstract

Even and odd Kählerian structures are constructed on supermanifolds associated with the tangent bundles of Kählerian manifolds. Mechanics that are bi-Hamiltonian with respect to the corresponding Poisson brackets are found; they determine Killing vectors of the Kählerian structures. An analog of the operator Δ in the Batalin—Vilkovisky quantization method is constructed; it corresponds to the divergence operator of the base manifold.

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References

  1. F. A. Berezin,Introduction to Algebra and Analysis with Anticommuting Variables [in Russian], Moscow State University, Moscow (1983).

    Google Scholar 

  2. D. A. Leites,Dokl. Akad. Nauk SSSR,236, 804 (1977).

    Google Scholar 

  3. O. M. Khudaverdian and R. L. Mkrtchian,Lett. Math. Phys.,18, 229 (1989).

    Google Scholar 

  4. I. A. Batalin and G. A. Vilkovisky,Phys. Lett. B.,102, 27 (1981).

    Google Scholar 

  5. I. A. Batalin and G. A. Vilkovisky,Nucl. Phys. B.,234, 106 (1984).

    Google Scholar 

  6. D. V. Volkov,Pis'ma Zh. Eksp. Teor. Fiz.,38, 508 (1983); D. V. Volkov, V. A. Soroka, and V. I. Tkach,Yad. Fiz.,44, 810 (1986).

    Google Scholar 

  7. D. V. Volkov, A. I. Pishnev, V. A. Soroka, and V. I. Tkach,Pis'ma Zh. Eksp. Teor. Fiz.,44, 55 (1986).

    Google Scholar 

  8. B. A. Kupersmidth,Lett. Math. Phys.,9, 323 (1985).

    Google Scholar 

  9. E. Witten,Mod. Phys. Lett. A.,5, 487 (1990).

    Google Scholar 

  10. O. M. Khudaverdian and A. P. Nersessian, “Formulation of Hamiltonian mechanics with odd and even Poisson brackets,” Preprint 1031(81)-87 [in Russian], Erevan Physics Institute, Erevan (1987).

    Google Scholar 

  11. O. M. Khudaverdian,J. Math. Phys.,32, 1934 (1991).

    Google Scholar 

  12. O. M. Khudaverdian and A. P. Nersessian,J. Math. Phys.,32, 1938 (1991).

    Google Scholar 

  13. V. Kac,Commun. Math. Phys.,53, 31 (1977).

    Google Scholar 

  14. A. P. Nersesyan and O. M. Khudaverdian,Izv. Akad. Nauk Arm. SSR Fiz.,25, 337 (1990).

    Google Scholar 

  15. V. N. Shander,Dokl. Akad. Nauk Bolgarii,36, 309 (1983).

    Google Scholar 

  16. O. M. Khudaverdian, A. S. Schwarz, and Yu. S. Tiupkin,Lett. Math. Phys.,5, 517 (1981).

    Google Scholar 

  17. M. A. Baranov and A. S. Shvarts,Funktsional Analiz i Ego Prilozhen.,18, 53 (1984).

    Google Scholar 

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Authors
  1. A. N. Nersesyan
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Additional information

Joint Institute for Nuclear Research, Dubna. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 96, No. 1, pp. 140–149, July, 1993.

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Nersesyan, A.N. On the geometry of supermanifolds with even and odd Kählerian structures. Theor Math Phys 96, 866–871 (1993). https://doi.org/10.1007/BF01074115

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  • DOI: https://doi.org/10.1007/BF01074115

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