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arXiv · 2205.03844

Real Hamiltonian forms of affine Toda field theories: spectral aspects

Vladimir S. Gerdjikov·Georgi G. Grahovski·Alexander A. Stefanov
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Abstract

The paper is devoted to real Hamiltonian forms of 2-dimensional Toda field theories related to exceptional simple Lie algebras, and to the spectral theory of the associated Lax operators. Real Hamiltonian forms are a special type of "reductions" of Hamiltonian systems, similar to real forms of semi-simple Lie algebras. Examples of real Hamiltonian forms of affine Toda field theories related to exceptional complex untwisted affine Kac-Moody algebras are studied. Along with the associated Lax representations, we also formulate the relevant Riemann-Hilbert problems and derive the minimal sets of scattering data that determine uniquely the scattering matrices and the potentials of the Lax operators.

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Vladimir S. Gerdjikov, Georgi G. Grahovski, Alexander A. Stefanov. 2022-05-08. Real Hamiltonian forms of affine Toda field theories: spectral aspects. https://doi.org/10.1134/s0040577922080037

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