https://doi.org/10.1140/epjb/e2002-00281-y
Complexifications and real forms of structures
1
Institute for Nuclear Research and Nuclear Energy, 72
Tzarigradsko chaussée, 1784 Sofia, Bulgaria
2
Dipartimento di
Fisica “E.R.Caianiello”, Universita di Salerno and Istituto
Nazionale di fisica Nucleare, Gruppo Collegato di Salerno, via S.
Aliende, Salerno, Italy
3
Dipartimento di Scienze Fisiche, Università Federico II di
Napoli and Istituto Nazionale di Fisica Nucleare, Sezione di
Napoli, Complesso Universitario di Monte Sant'Angelo, Via Cintia,
80126 Napoli, Italy
Corresponding author: a gerjikov@inrne.bas.bg
Received:
18
October
2001
Revised:
24
May
2002
Published online:
2
October
2002
We consider generalizations of the standard dynamics to complex dynamical variables and introduce the notions of real form in analogy with the notion of real forms for a simple Lie algebra. Thus to each real 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 system (e.g. the Toda chain) one can complexify it and then project onto different real forms.
PACS: 02.30.Ik – Integrable systems / 02.40.Tt – Complex manifolds / 45.20.Jj – Lagrangian and mechanics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2002