Abstract:
We consider generalizations of the standard Hamiltonian dynamics to complex dynamical variables and introduce the notions of real Hamiltonian form in analogy with the notion of real forms for a simple Lie algebra. Thus to each real Hamiltonian system we are able to relate several nonequivalent ones. On the example of the complex Toda chain we demonstrate how starting from a known integrable Hamiltonian system (e.g. the Toda chain) one can complexify it and then project onto different real forms.
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Received 18 October 2001 / Received in final form 24 May 2002 Published online 2 October 2002
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Gerdjikov, V., Kyuldjiev, A., Marmo, G. et al. Complexifications and real forms of Hamiltonian structures. Eur. Phys. J. B 29, 177–181 (2002). https://doi.org/10.1140/epjb/e2002-00281-y
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DOI: https://doi.org/10.1140/epjb/e2002-00281-y