Skip to main content
SpringerLink
Log in

Quantum Hamiltonians associated with finite-dimensional Lie algebras and factorized s-matrices

  • 2. Completely Integrable Systems
  • Conference paper
  • First Online:
The Riemann Problem, Complete Integrability and Arithmetic Applications

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 925))

  • 463 Accesses

Abstract

We consider quantum Hamiltonian systems of lattice type which are associated with classical finite dimensional Lie algebras (like MH(2), SO(3) etc.), and possess complete integrability properties. These Hamiltonian systems are written in canonical Heisenberg pn, qn variables. They have factorized S-matrices and are generalizations of the quantum Toda lattice Hamiltonian as well as XYZ-models of statistical mechanics.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. E.T. Whittaker, A treatise on the analytical dynamics of particles and rigid bodies, Cambridge, 1927.

    Google Scholar 

  2. M. Gutzwiller, Ann. of Physics 124, 347 (1980); Ann. of Physics (1981) (to appear).

    Google Scholar 

  3. A.A. Kirillov, Representation Theory, Springer 1972. R. Gilmore, Lie Groups, Lie Algebras and some of their applications, John Wiley, 1974.

    Google Scholar 

  4. L. Onsager, Phys. Rev. 65, 117 (1944). C.J. Thompson, Mathematical statistical mechanics, Princeton Univ. Press. 1972. J.M. Drouffe, C. Itzykson, Phys. Repts. 38C, 133 (1975).

    Article  MathSciNet  Google Scholar 

  5. R. Baxter, Ann. Phys. 76, 1, 25, 48 (1973).

    Article  MathSciNet  Google Scholar 

  6. D.V. Chudnovsky, G.V. Chudnovsky, Phys. Lett., 98B, 83 (1981), Phys. Lett., 79A, 36 (1980).

    Article  MathSciNet  Google Scholar 

  7. Here G[[Ï•]] denotes the formal power series in Ï• with the coefficients from G.

    Google Scholar 

  8. D.V. Chudnovsky, G.V. Chudnovsky, Lett. Math. Phys. 5, 43 (1981). (EN-Saclay Prepring DPh-T/80/131, September 1980 (to appear)).

    Article  MathSciNet  Google Scholar 

  9. R.J. Baxter, Trans. Royal Soc. London, A289, 315 (1978); R.J. Baxter, Academic Press (to appear).

    Article  MathSciNet  Google Scholar 

  10. N. Bourbaki, Groupes et algèbres de Lie, Herman, Paris, 1968.

    MATH  Google Scholar 

  11. A.B. Zamolodchikov, Comm. Math. Phys. 69, 165 (1979). b) E.K. Sklanin, L.A. Takhtadjan, L.D. Faddeev, Theor. Math. Phys. 40, 688 (1980). L. Takhtadjan, L.D. Faddeev, Usp. Mat. Nauk. 34, 13, 1979.

    Article  MathSciNet  Google Scholar 

  12. R.M. Case, J. Math. Phys., 15, 2166 (1974). K.M. Case, M. Kac, J. Math. Phys., 14, 594 (1973).

    Article  MathSciNet  Google Scholar 

  13. E.T. Whittaker, Watson, A course of modern analysis, v. 2, Cambridge Univ. Press, 1927. *** DIRECT SUPPORT *** A00J4399 00006

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Columbia University, New York, NY, USA

    D.V. Chudnovsky & G.V. Chudnovsky

Authors
  1. D.V. Chudnovsky
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G.V. Chudnovsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

David V. Chudnovsky Gregory V. Chudnovsky

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Springer-Verlag

About this paper

Cite this paper

Chudnovsky, D., Chudnovsky, G. (1982). Quantum Hamiltonians associated with finite-dimensional Lie algebras and factorized s-matrices. In: Chudnovsky, D.V., Chudnovsky, G.V. (eds) The Riemann Problem, Complete Integrability and Arithmetic Applications. Lecture Notes in Mathematics, vol 925. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0093506

Download citation

  • DOI: https://doi.org/10.1007/BFb0093506

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11483-3

  • Online ISBN: 978-3-540-39152-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation