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SUMMARY:Integrable spinor models in two dimensional space-time
DTSTART;VALUE=DATE-TIME:20220726T153000Z
DTEND;VALUE=DATE-TIME:20220726T170000Z
DTSTAMP;VALUE=DATE-TIME:20261014T201000Z
UID:indico-event-23@indico.iaps.institute
CONTACT:info@iaps.institute\;academy@quanterall.com\;+359 879411009
DESCRIPTION:Speakers: Владимир Герджиков (Institute for A
 dvanced Physical Studies)\nSeveral spinor models were proposed several dec
 ades ago in the efforts to explain the nature of strong interactions\, see
  [1]. These are\n• Nambu--Jona-Lasinio--Vaks--Larkin models (1961)\, rel
 ated to SU(n)\n• Gross–Neveu models (1974)\, related to SP(2n).\n• Z
 akharov– Mikhailov spinor models (1980) related to SO(n).\n\nFollowing [
 1] we will analyze their reductions to two-dimensional space-time and will
  explain how they could be integrated explicitly. We will start by constru
 cting their Lax representations. Then the spectral properties of their Lax
  operators will be outlined. Using the dressing Zakharov-Shabat method we 
 will construct their soliton solutions. Other integrable deformations of t
 hese models will be formulated following [2].\n\nThe lectures will take p
 lace each Tuesday\, 18:30 EET. For participants residing in Sofia it is g
 ood to attend the lectures in person at Sofia Tech Park\, Laboratory compl
 ex. The online participation is at https://meet.iaps.institute/integrable
 -spinor-models.\n\n\nReferences\n[1] V. E. Zakharov and A. V. Mikhailov. O
 n the Integrability of Classical Spinor Models in Two- Dimensional Space-T
 ime. Commun. Math. Phys. 74\, 2140 (1980).\n[2] V. S. Gerdjikov. Z2-reduct
 ions of spinor models in two dimensions. arXiv:1210.3722v1 [nlin.SI]\n\n[3
 ]  В. Е. Захаров\, А. Б. Шабат\, “Интегрир
 ование нелинейных уравнений математиче
 ской физики методом обратной задачи рас
 сеяния. II”\, Функц. анализ и его прил.\, 13
 :3 (1979)\, 13–22\; Funct. Anal. Appl.\, 13:3 (1979)\, 166–174\n\n
  \n\n==============================\n\n \n\nLecture 1. July 26th\, 2022.
  Lax representation and Nambu-Jona-Lasinio-Vaks-Larkin\, Gross-Neveu and
  Zakharov-Mikhailov models\, slides\, video (damaged recording\; chang
 e the video player if interruptions occur) \n\nLecture 2. August 2nd\, 20
 22\, The inverse scattering method\, slides\, video\n\nLecture 3. August 9
 th\, 2022\, Zakharov -- Shabat dressing method and soliton solutions. So
 liton solutions of the Nambu--Jona-Lasinio--Vaks--Larkin model\, slides\, 
 video\n\nLecture 4. August 16th\, 2022\, Lax representations and simple Li
 e algebras\, slides\, video\n\nLecture 5. August 23rd\, 2022\, Lax represe
 ntations\, simple Lie algebras and spinor models\, slides\, video (damage
 d recording\; change the video player if interruptions occur)\n\nLecture 
 6. August 30th\, 2022\, Riemann-Hilbert problems and soliton solutions of 
 Zakharov--Mikhailov models\, slides\, video.\nhttps://indico.iaps.institut
 e/event/23/
LOCATION:Лабораторен комплекс  (София тех па
 рк)
URL:https://indico.iaps.institute/event/23/
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