Skip to main content
Log in

On new realizations of the poincare groups P (1,2) and P(2, 2)

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We classify realizations of the Poincare groups P (1, 2) and P (2, 2) in the class of local Lie groups of transformations and obtain new realizations of the Lie algebras of infinitesimal operators of these groups.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. V. G. Kadyshevskii, “Quantum field theory and momentum space of constant curvature,” in: Problems of Theoretical Physics [in Russian], Nauka, Moscow (1972), pp. 52–73.

    Google Scholar 

  2. J. J. Aghassi, P. Roman, and R. M. Santilli, “Relation of the inhomogeneous de Sitter group to the quantum mechanics of elementary particles,” J. Math. Phys., 11, No. 8, 2297–2301 (1970).

    Article  MathSciNet  Google Scholar 

  3. R. M. Mir-Kasimov, “Representations of the de Sitter group and quantum field theory in the quantized space-time,” in: Proceeding of the International Seminar “Group-Theoretical Methods in Physics (Zvenigorod, 1979) [in Russian], Vol. 1, Nauka, Moscow (1980), pp. 198–201.

    Google Scholar 

  4. L. V. Ovsyannikov, Group Analysis of Differential Equations [in Russian] Nauka, Moscow 1978.

    MATH  Google Scholar 

  5. V. I. Fushchich and A. G. Nikitin, Symmetry of Equations of Quantum Mechanics [in Russian] Nauka, Moscow 1990.

    MATH  Google Scholar 

  6. W. Fushchych, W. Shtelen, and N. Serov, Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics, Kluwer, Dordrecht (1993).

    Google Scholar 

  7. W. I. Fushchych and R. Z. Zhdanov, Symmetry and Exact Solutions of Nonlinear Dirac Equations, Mat. Ukr. Publ., Kiev (1997).

    Google Scholar 

  8. T. A. Ivanova and A. D. Popov, “Some new integrable equations from the self-dual Yang-Mills equations,” Phys. Lett. A, 205, 158–166 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  9. G. Rideau and P. Winternitz, “Nonlinear equations invariant under the Poincare, similitude, and conformal groups in two-dimensional space-time,” J. Math. Phys., 31, No. 5, 1095–1105 (1990).

    Article  MATH  MathSciNet  Google Scholar 

  10. V. I. Fushchich and V. I. Lagno, “On new nonlinear equations invariant under the Poincare group in two-dimensional space-time,” Dop. Nats. Akad. Nauk Ukr., No. 11, 60–65 (1996).

    Google Scholar 

  11. W. I. Fushchych and I. A. Egorchenko, “Second-order differential invariants of the rotation group O(n) and of its extensions E(n), P( 1, n), and G( 1, n),” Acta Appl. Math., 28, 69–92 (1992).

    MathSciNet  Google Scholar 

  12. I. A. Egorchenko, “Nonlinear representations of the Poincare” algebra and invariant equations,” in: Symmetry Analysis of Equations of Mathematical Physics, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1992), pp. 62–65.

    Google Scholar 

  13. W. Fushchych, R. Zhdanov, and V. Lagno, “On linear and nonlinear representations of the generalized Poincare groups in the class of Lie vector fields,” J. Nonlin. Math. Phys., 1, No. 3, 295–308 (1994).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhdanov, R.Z., Lagno, V.I. On new realizations of the poincare groups P (1,2) and P(2, 2). Ukr Math J 52, 513–530 (2000). https://doi.org/10.1007/BF02515394

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02515394

Keywords

Navigation