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2009 | 115 | 1 | 159-161
Article title

Bethe Ansatz and Geometry of the Classical Configuration Space

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Abstracts
EN
We demonstrate that the seminal one-dimensional model of the Heisenberg magnet, consisting of N spins 1/2 with the nearest-neighbour isotropic interaction, solved exactly by Bethe ansatz, admits an interpretation of a system of r=N/2-M pseudoparticles (spin deviations) which are indistinguishable, have hard cores and move on the chain by local hoppings. Such an approach allows us to construct a manifold with some boundaries, which is genericly r-dimensional, and whose F-dimensional regions, 0
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Contributors
author
  • Chair of Physics, Rzeszów University of Technology, Powstańców Warszawy 6, 35-959 Rzeszów, Poland
author
  • Chair of Physics, Rzeszów University of Technology, Powstańców Warszawy 6, 35-959 Rzeszów, Poland
author
  • Institute of Mathematics, Poznań University of Technology, Piotrowo 3A, 60-965 Poznań, Poland
References
  • 1. H. Bethe, Z. Phys. 71, 205 (1931) (in German; English translation in: D.C. Mattis, The Many-Body Problem, World Sci., Singapore 1993, p. 689)
  • 2. M. Gaudin, Le Fonction d'Onde de Bethe, Massons, Paris 1983
  • 3. R.J. Baxter, Exactly Solvable Models in Statistical Mechanics, Academic Press, New York 1982
  • 4. J. Schwinger, Quantum Kinematics and Dynamics, Benjamin, New York 1970
  • 5. A. Vourdas, J. Phys. A, Math. Gen. 29, 4275 (1996)
  • 6. A. Vourdas, J. Phys. A, Math. Theor. 40, R285 (2007)
  • 7. S.V. Kerov, A.N. Kirillov, N.Yu. Reshetikhin, Leningradskoe Otdeleniye Matematicheskogo Instituta im. V.A. Steklova AN SSSR (LOMI) 155, 50 (1986) (in Russian; English translation: J. Sov. Math. 41, 916 (1988)
  • 8. A. Schilling, MSJ Memoirs 17, 75 (2007)
  • 9. T. Lulek, B. Lulek, D. Jakubczyk, P. Jakubczyk, Physica B: Phys. Condens. Matter 382, 162 (2006)
  • 10. B. Lulek, T. Lulek, Rep. Math. Phys. 38, 267 (1996)
  • 11. J. Milewski, B. Lulek, T. Lulek, Phys. Status Solidi B 244, 2497 (2007)
Document Type
Publication order reference
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YADDA identifier
bwmeta1.element.bwnjournal-article-appv115n1040kz
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