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SUMMARY:On real Hamiltonian forms of affine Toda  field theories - Georg
 i Grahovski (University of Essex)
DTSTART:20221005T143000Z
DTEND:20221005T153000Z
UID:TALK182831@talks.cam.ac.uk
DESCRIPTION:We will present real Hamiltonian forms of 2-dimensional Toda 
  field theories related to exceptional simple Lie algebras [1]\, and the
  spectral theory of the associated Lax operators. Real&nbsp\;Hamiltonian f
 orms [2] are a special type of "reductions" of Hamiltonian systems\, simil
 ar to&nbsp\;real forms of semi-simple Lie algebras. Examples of real Hamil
 tonian forms of affine Toda  field&nbsp\;theories related to exceptional
  complex untwisted affine Kac-Moody algebras will be presented.&nbsp\;Alon
 g with the associated Lax representations\, we will also discuss the relev
 ant Riemann-&nbsp\;Hilbert problems and derive the minimal sets of scatter
 ing data that determine uniquely the&nbsp\;scattering matrices and the pot
 entials of the Lax operators.\n&nbsp\;\nThis is a joint work [3] with Vlad
 imir Gerdjikov and Alexander Stefanov.\n&nbsp\;\n&nbsp\;\nReferences\n[1] 
 V. S. Gerdjikov and G. G. Grahovski\, On reductions and real Hamiltonian f
 orms of affine&nbsp\;Toda  eld theories\, J Nonlin. Math. Phys. 12 (2005
 )\, Suppl. 3\,&nbsp\;153-168\nV. S. Gerdjikov and G. G. Grahovski\, Real H
 amiltonian Forms of Affine Toda Models&nbsp\;Related to Exceptional Lie Al
 gebras\, SIGMA 2 (2006)\,&nbsp\;paper 022&nbsp\;(11 pages)\n&nbsp\;\n[2] V
 . S. Gerdjikov\, A. V. Kyuldjiev\, G. Marmo and G. Vilasi\, Complexificati
 ons and Real&nbsp\;Forms of Hamiltonian Structures\, European J. Phys. B 2
 9 (2002)&nbsp\;177-182\;\nV. S. Gerdjikov\, A. V. Kyuldjiev\, G. Marmo and
  G. Vilasi\, Real Hamiltonian forms of Hamiltonian systems\, European Phys
 . J. B. 38 (2004)&nbsp\;635-649\n&nbsp\;\n[3] V. S. Gerdjikov\, G. G. Grah
 ovski and A. A. Stefanov\, Real Hamiltonian forms of affine&nbsp\;Toda  
 field theories: spectral aspects\, Theor. Math. Phys. 212 (2022)&nbsp\;105
 3-1072&nbsp\;[E-print:&nbsp\;arXiv:2205.03844].
LOCATION:Seminar Room 1\, Newton Institute
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