Real Hamiltonian forms of affine Toda field theories: spectral aspects
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866929288978104320 |
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| author | Gerdjikov, Vladimir S. Grahovski, Georgi G. Stefanov, Alexander A. |
| author_facet | Gerdjikov, Vladimir S. Grahovski, Georgi G. Stefanov, Alexander A. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2205_03844 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Real Hamiltonian forms of affine Toda field theories: spectral aspects Gerdjikov, Vladimir S. Grahovski, Georgi G. Stefanov, Alexander A. Exactly Solvable and Integrable Systems High Energy Physics - Theory Mathematical Physics 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. |
| title | Real Hamiltonian forms of affine Toda field theories: spectral aspects |
| topic | Exactly Solvable and Integrable Systems High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2205.03844 |