Real Hamiltonian Forms of Affine Toda Models Related to Exceptional Lie Algebras

Details Real Hamiltonian Forms of Affine Toda Models Related to Exceptional Lie Algebras Real Hamiltonian Forms of Affine Toda Models Related to Exceptional Lie Algebras

2006-02-17

arxiv.org/abs/nlin/0602038v1

SIGMA 2 (2006), 022, 11 pages

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

Scientific paper

10.3842/SIGMA.2006.022

The construction of a family of real Hamiltonian forms (RHF) for the special class of affine 1+1-dimensional Toda field theories (ATFT) is reported. Thus the method, proposed in [1] for systems with finite number of degrees of freedom is generalized to infinite-dimensional Hamiltonian systems. The construction method is illustrated on the explicit nontrivial example of RHF of ATFT related to the exceptional algebras E_6 and E_7. The involutions of the local integrals of motion are proved by means of the classical R-matrix approach.

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