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Обзоры актуальных проблем


Интегрируемость и матричные модели


Государственный научный центр Российской Федерации «Институт теоретической и экспериментальной физики им. А.И. Алиханова», ул. Б. Черемушкинская 25, Москва, 117259, Российская Федерация

Обзор теории матричных моделей с точки зрения ее связи с интегрируемыми иерархиями. Приведен весьма подробный анализ дискретных одноматричных, двухматричных «конформных» (многокомпонентных) моделей и модели Концевича, а также тождеств Уорда (’W-условий’), детерминантных формул и непрерывных пределов, переводящих один вид моделей в другой. Обсуждаются вопросы, требующие дополнительной разработки, а также направления дальнейших исследований.

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English fulltext is available at DOI: 10.1070/PU1994v037n01ABEH000001
PACS: 02.10.+b, 11.17.+y
DOI: 10.3367/UFNr.0164.199401a.0003
URL: https://ufn.ru/ru/articles/1994/1/a/
A1994NA86300001
Цитата: Морозов А Ю "Интегрируемость и матричные модели" УФН 164 3–62 (1994)
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English citation: Morozov A Yu “Integrability and matrix modelsPhys. Usp. 37 1–55 (1994); DOI: 10.1070/PU1994v037n01ABEH000001

Список литературы (113) Статьи, ссылающиеся на эту (217) ↓ Похожие статьи (20)

  1. Mishnyakov V, Morozov A, Reva M Nuclear Physics B 1010 116746 (2025)
  2. Li Ch, Mironov A, Orlov A Yu Physics Letters B 860 139170 (2025)
  3. Morozov A Encyclopedia of Mathematical Physics (2025) p. 168
  4. Drachov Ya, Mironov A, Popolitov A Physics Letters B 849 138426 (2024)
  5. Eynard B, Garcia-Failde E et al Ann. Henri Poincaré (2024)
  6. Galakhov D, Morozov A, Tselousov N Phys. Rev. D 109 (6) (2024)
  7. Mironov A, Mishnyakov V, Morozov A Nuclear Physics B 1001 116504 (2024)
  8. Mironov A, Morozov A, Popolitov A Phys. Rev. D 110 (12) (2024)
  9. Morozov A, Oreshina A Physics Letters B 857 139006 (2024)
  10. Mironov A, Oreshina A, Popolitov A Eur. Phys. J. C 84 (7) (2024)
  11. Kubo N, Nosaka T J. High Energ. Phys. 2024 (7) (2024)
  12. Mironov A, Morozov A et al Phys. Rev. D 110 (4) (2024)
  13. Na W, Yang B et al Adv. Appl. Clifford Algebras 33 (1) (2023)
  14. Mironov A, Mishnyakov V et al Eur. Phys. J. C 83 (5) (2023)
  15. Mironov A, Morozov A J. High Energ. Phys. 2023 (3) (2023)
  16. Mishnyakov V, Morozov A, Suprun P Nuclear Physics B 992 116245 (2023)
  17. Barseghyan S, Popolitov A Annals of Physics 449 169207 (2023)
  18. Wang N Reports on Mathematical Physics 91 79 (2023)
  19. Drachov Ya, Zhabin A Eur. Phys. J. C 83 (5) (2023)
  20. Morozov A, Tselousov N J. High Energ. Phys. 2023 (11) (2023)
  21. Morozov A Eur. Phys. J. C 83 (3) (2023)
  22. Vleeshouwers W L, Gritsev V J. Phys. A: Math. Theor. 56 185002 (2023)
  23. Liu F, Mironov A et al Nuclear Physics B 993 116283 (2023)
  24. Wang G J. High Energ. Phys. 2023 (3) (2023)
  25. Wang N 63 (12) (2022)
  26. Mishnyakov V, Oreshina A Eur. Phys. J. C 82 (6) (2022)
  27. Wang N, Wu K Nuclear Physics B 974 115642 (2022)
  28. Mironov A, Mishnyakov V et al Physics Letters B 829 137041 (2022)
  29. Balthazar B, Giveon A et al J. High Energ. Phys. 2022 (1) (2022)
  30. Mishnyakov V, Suprun P Jetp Lett. 115 477 (2022)
  31. Mironov A, Morozov A, Popolitov A Physics Letters B 824 136833 (2022)
  32. Mironov A, Morozov A, Zakirova Z Physics Letters B 831 137178 (2022)
  33. Mironov A, Morozov A, Popolitov A Physics Letters B 828 137038 (2022)
  34. Wang N, Wu K 63 (2) (2022)
  35. Lanina E, Morozov A Eur. Phys. J. C 82 (11) (2022)
  36. Mironov A, Morozov A Physics Letters B 835 137573 (2022)
  37. Mironov A, Morozov A Phys. Rev. D 106 (12) (2022)
  38. Mironov A, Mishnyakov V et al Nuclear Physics B 985 116022 (2022)
  39. Khlaif O, Kimura T J. High Energ. Phys. 2022 (4) (2022)
  40. Wang R, Zhang Ch-H et al Nuclear Physics B 985 115989 (2022)
  41. Cui Zh, Bai Ya et al Nuclear Physics B 984 115986 (2022)
  42. Anokhina A S Phys. Part. Nuclei 52 374 (2021)
  43. Mironov A, Morozov A Physics Letters B 816 136268 (2021)
  44. Altland A, Sonner Ju SciPost Phys. 11 (2) (2021)
  45. Araujo T Nuclear Physics B 972 115566 (2021)
  46. Mironov A D, Morozov A Physics Letters B 819 136474 (2021)
  47. Okuyama K, Sakai K J. High Energ. Phys. 2021 (9) (2021)
  48. Mironov A, Morozov A Physics Letters B 816 136221 (2021)
  49. Mironov A, Mishnyakov V, Morozov A Physics Letters B 823 136721 (2021)
  50. Beccaria M, Tseytlin A A J. High Energ. Phys. 2021 (1) (2021)
  51. Mironov A, Morozov A Physics Letters B 816 136196 (2021)
  52. Mironov A, Morozov A Eur. Phys. J. C 81 (3) (2021)
  53. Mironov A D, Morozov A et al Lett Math Phys 111 (5) (2021)
  54. Mironov A, Mishnyakov V et al Jetp Lett. 113 728 (2021)
  55. Morozov A J. High Energ. Phys. 2021 (10) (2021)
  56. Beccaria M, Hasan A J. High Energ. Phys. 2021 (4) (2021)
  57. Mironov A, Morozov A J. High Energ. Phys. 2021 (2) (2021)
  58. Mironov A, Mishnyakov V et al Eur. Phys. J. C 81 (12) (2021)
  59. Tian K, Li S et al Physics Letters B 822 136643 (2021)
  60. Anokhina A S Phys. Part. Nuclei 51 172 (2020)
  61. Lodin R, Popolitov A et al Lett Math Phys 110 179 (2020)
  62. Morozov A, Popolitov A, Shakirov Sh Physics Letters B 811 135932 (2020)
  63. Orlov A Yu Geometric Methods in Physics XXXVIII Trends in Mathematics Chapter 15 (2020) p. 221
  64. Morozov A, Tselousov N Eur. Phys. J. C 80 (12) (2020)
  65. Dubrovin B, Liu S-Q et al Commun. Math. Phys. 379 461 (2020)
  66. Cassia L, Lodin R, Zabzine M J. High Energ. Phys. 2020 (10) (2020)
  67. Morozov A Eur. Phys. J. C 79 (1) (2019)
  68. Morozov A Physics Letters B 792 205 (2019)
  69. Mironov A, Morozov A, Zakirova Z J. High Energ. Phys. 2019 (10) (2019)
  70. Nieri F, Pan Y, Zabzine M Commun. Math. Phys. 366 397 (2019)
  71. Li Ch-X, Qin Zh-Yu, Shen Sh-F J. Phys. Soc. Jpn. 88 124003 (2019)
  72. Cassia L, Lodin R et al J. High Energ. Phys. 2019 (12) (2019)
  73. Itoyama H, Mironov A, Morozov A Physics Letters B 788 76 (2019)
  74. Nieri F, Pan Y et al EPJ Web Conf. 191 06005 (2018)
  75. van de Leur J W, Orlov A Yu J. Phys. A: Math. Theor. 51 025208 (2018)
  76. Itoyama H, Mironov A, Morozov A Nuclear Physics B 932 52 (2018)
  77. Ivanitskii G R Phys.-Usp. 61 871 (2018)
  78. Mironov A, Morozov A Physics Letters B 785 207 (2018)
  79. Morozov A Physics Letters B 785 175 (2018)
  80. Morozov A, Popolitov A, Shakirov Sh Physics Letters B 784 342 (2018)
  81. Betzios P, Gürsoy U, Papadoulaki O Nuclear Physics B 928 356 (2018)
  82. Mironov A, Morozov A J. High Energ. Phys. 2018 (8) (2018)
  83. Nedelin A, Zabzine M J. High Energ. Phys. 2017 (3) (2017)
  84. Itoyama H, Mironov A, Morozov A J. High Energ. Phys. 2017 (6) (2017)
  85. Ivanitskii G R Успехи физических наук 187 757 (2017)
  86. [Ivanitskii G R Phys.-Usp. 60 705 (2017)]
  87. Nedelin A, Nieri F, Zabzine M Commun. Math. Phys. 353 1059 (2017)
  88. Itoyama H, Mironov A, Morozov A Physics Letters B 771 180 (2017)
  89. Mironov A, Morozov A Physics Letters B 774 210 (2017)
  90. Mironov A, Morozov A Physics Letters B 771 503 (2017)
  91. Melnikov D, Mironov A, Morozov A J. High Energ. Phys. 2016 (5) (2016)
  92. Morozov A, Zenkevich Y J. High Energ. Phys. 2016 (2) (2016)
  93. Popolitov A Jetp Lett. 103 137 (2016)
  94. Awata H, Kanno H et al J. High Energ. Phys. 2016 (7) (2016)
  95. Natanzon S M, Zabrodin A V J. Phys. A: Math. Theor. 49 145206 (2016)
  96. Ding X-M, Li Yu, Meng L J. High Energ. Phys. 2016 (1) (2016)
  97. Procházka Tomáš J. High Energ. Phys. 2016 (10) (2016)
  98. Morozov A A Phys. Part. Nuclei 47 775 (2016)
  99. Mironov A, Morozov A, Zenkevich Y Physics Letters B 762 196 (2016)
  100. Lafortune S, Li Ch-X J. Phys. A: Math. Theor. 49 475202 (2016)
  101. Morozov A, Morozov A, Popolitov A Physics Letters B 749 309 (2015)
  102. Alexandrov A J. High Energ. Phys. 2015 (3) (2015)
  103. Mironov A, Morozov A et al Int. J. Mod. Phys. A 30 1550169 (2015)
  104. Kanning N, Ko Yu, Staudacher M Nuclear Physics B 894 407 (2015)
  105. Kanzieper E Constr Approx 41 615 (2015)
  106. Itoyama H, Yoshioka R Prog. Theor. Exp. Phys. 2015 11B103 (2015)
  107. Alexandrov A, Mironov A et al J. High Energ. Phys. 2014 (11) (2014)
  108. Orlov A Yu Physics Letters A 378 319 (2014)
  109. Kimura T Progress of Theoretical and Experimental Physics 2014 123A01 (2014)
  110. Alexandrov A, Leurent S et al Nuclear Physics B 883 173 (2014)
  111. Alexandrov A Lett Math Phys 104 75 (2014)
  112. Alexandrov A, Mironov A et al Jetp Lett. 100 271 (2014)
  113. Kimura T Progress of Theoretical and Experimental Physics 2014 103B04 (2014)
  114. Mironov A, Morozov A, Sleptsov A Eur. Phys. J. C 73 (7) (2013)
  115. Alexandrov A, Zabrodin A Journal of Geometry and Physics 67 37 (2013)
  116. Li M, Li Ch et al 54 (4) (2013)
  117. Галахов Д В, Galakhov D V и др ТМФ 172 73 (2012)
  118. MIRONOV A, MOROZOV A, SHAKIROV SH Int. J. Mod. Phys. A 27 1230001 (2012)
  119. Морозов А Ю, Morozov A Yu Теоретическая и математическая физика 173 104 (2012)
  120. Mironov A, Morozov A, Natanzon S Journal of Geometry and Physics 62 148 (2012)
  121. Alexandrov A J. Phys.: Conf. Ser. 343 012009 (2012)
  122. Alexandrov A, Mironov A et al J. Phys. A: Math. Theor. 45 045209 (2012)
  123. Itoyama H, Mironov A et al J. High Energ. Phys. 2012 (7) (2012)
  124. Mironov A, Morozov A, Zakirova Z Physics Letters B 711 332 (2012)
  125. Takasaki K, Takebe T Anal.Math.Phys. 2 171 (2012)
  126. Brown T W Phys. Rev. D 83 (8) (2011)
  127. Tian KeLei, He JingSong et al Sci. China Math. 54 257 (2011)
  128. Morozov A, Shakirov Sh Journal of Geometry and Physics 61 708 (2011)
  129. ALEXANDROV A Mod. Phys. Lett. A 26 2193 (2011)
  130. Mironov A, Morozov A, Shakirov Sh J. High Energ. Phys. 2011 (2) (2011)
  131. Alexandrov A Nuclear Physics B 851 620 (2011)
  132. Миронов А Д, Mironov A D и др ТМФ 166 3 (2011) [Mironov A D, Morozov A Yu, Natanzon S M Theor Math Phys 166 1 (2011)]
  133. Shakirov Sh Physics Letters A 375 984 (2011)
  134. Tian K, Hea J et al Chin. Ann. Math. Ser. B 32 895 (2011)
  135. Mironov A, Morozov A, Shakirov Sh J. High Energ. Phys. 2011 (3) (2011)
  136. Mironov A, Morozov A, Morozov A Nuclear Physics B 843 534 (2011)
  137. Mironov A, Morozov A J. Phys. A: Math. Theor. 43 195401 (2010)
  138. MIRONOV A, MOROZOV A, SHAKIROV SH Int. J. Mod. Phys. A 25 3173 (2010)
  139. Морозов А Ю, Morozov A Yu ТМФ 162 3 (2010) [Morozov A Yu Theor Math Phys 162 1 (2010)]
  140. Mironov A, Morozov A, Shakirov Sh J. High Energ. Phys. 2010 (2) (2010)
  141. Mironov A, Morozov A J. High Energ. Phys. 2010 (4) (2010)
  142. Mironov A, Mironov S et al J. Phys. A: Math. Theor. 43 055402 (2010)
  143. Osipov V A, Kanzieper E Annals of Physics 325 2251 (2010)
  144. Mironov A, Morozov A J. High Energy Phys. 2009 024 (2009)
  145. Morozov A, Shakirov Sh J. High Energy Phys. 2009 003 (2009)
  146. Dimakis A, Müller-Hoissen F Generalized Lie Theory in Mathematics, Physics and Beyond Chapter 2 (2009) p. 9
  147. Wang D 50 (7) (2009)
  148. Akhmedov E T Phys. Atom. Nuclei 72 1574 (2009)
  149. Mironov A, Morozov A Physics Letters B 680 188 (2009)
  150. Osipov V A, Kanzieper E J. Phys. A: Math. Theor. 42 475101 (2009)
  151. Morozov A, Shakirov Sh J. High Energy Phys. 2009 002 (2009)
  152. ALEXANDROV A, MIRONOV A et al Int. J. Mod. Phys. A 24 4939 (2009)
  153. Alexandrov A, Mironov A, Morozov A J. High Energy Phys. 2009 053 (2009)
  154. MOROZOV A, SHAKIROV SH Mod. Phys. Lett. A 24 2659 (2009)
  155. Morozov A, Shakirov Sh J. High Energy Phys. 2009 064 (2009)
  156. Galakhov D, Itoyama H et al Nuclear Physics B 823 289 (2009)
  157. Morozov A J. High Energy Phys. 2008 086 (2008)
  158. DOLOTIN V, MOROZOV A Int. J. Mod. Phys. A 23 3613 (2008)
  159. Морозов А Ю, Morozov A Yu ТМФ 157 208 (2008) [Morozov A Yu Theor Math Phys 157 1542 (2008)]
  160. Kostov I K, Petkova V B Nuclear Physics B 769 175 (2007)
  161. Александров А С, Alexandrov A S и др ТМФ 150 179 (2007) [Alexandrov A S, Mironov A D, Morozov A Yu Theor Math Phys 150 153 (2007)]
  162. Alexandrov A, Mironov A, Morozov A Physica D: Nonlinear Phenomena 235 126 (2007)
  163. Okuyama K Physics Letters B 645 275 (2007)
  164. ALEXANDROV A, MIRONOV A, MOROZOV A Int. J. Mod. Phys. A 21 2481 (2006)
  165. Чехов Л О, Chekhov L O и др УМН 61 93 (2006)
  166. Ellwood I, Hashimoto A J. High Energy Phys. 2006 002 (2006)
  167. Chekhov L J. Phys. A: Math. Gen. 39 8857 (2006)
  168. Zabrodin A NATO Science Series II: Mathematics, Physics and Chemistry Vol. Applications of Random Matrices in PhysicsMATRIX MODELS AND GROWTH PROCESSES: FROM VISCOUS FLOWS TO THE QUANTUM HALL EFFECT221 Chapter 8 (2006) p. 261
  169. Sedrakyan T A Nuclear Physics B 729 526 (2005)
  170. Morozov A NATO Science Series II: Mathematics, Physics and Chemistry Vol. String Theory: From Gauge Interactions to CosmologyChallenges of Matrix Models208 Chapter 6 (2005) p. 129
  171. Александров А С, Alexandrov A S и др ТМФ 142 419 (2005) [Alexandrov A S, Mironov A D, Morozov A Yu Theor Math Phys 142 349 (2005)]
  172. Orlov A Yu Acta Appl Math 86 131 (2005)
  173. Klemm A Fortschritte der Physik 53 720 (2005)
  174. Okuyama K J. High Energy Phys. 2005 002 (2005)
  175. Maldacena Ju, Moore G et al J. High Energy Phys. 2004 020 (2004)
  176. Konopelchenko B G, Moro A J. Phys. A: Math. Gen. 37 L105 (2004)
  177. YU ORLOV A Int. J. Mod. Phys. A 19 276 (2004)
  178. ALEXANDROV A, MOROZOV A, MIRONOV A Int. J. Mod. Phys. A 19 4127 (2004)
  179. Chiantese S, Klemm A, Runkel I J. High Energy Phys. 2004 033 (2004)
  180. JURČO BRANISLAV Mod. Phys. Lett. A 19 1661 (2004)
  181. Миронов А Д, Mironov A D и др ТМФ 135 434 (2003)
  182. Itoyama H, Morozov A Nuclear Physics B 657 53 (2003)
  183. Fyodorov Ya V, Strahov E J. Phys. A: Math. Gen. 36 3203 (2003)
  184. Zinn-Justin P, Zuber J-B J. Phys. A: Math. Gen. 36 3173 (2003)
  185. Dymarsky A, Pestun V Phys. Rev. D 67 (12) (2003)
  186. Morozov A, Niemi A J Nuclear Physics B 666 311 (2003)
  187. Konopelchenko B, Moro A J. Phys. A: Math. Gen. 36 11837 (2003)
  188. Gorbunov I V, Sharapov A A Physics Letters B 531 255 (2002)
  189. Marshakov A V Uspekhi Fizicheskikh Nauk 172 977 (2002)
  190. Dijkgraaf R, Vafa C Nuclear Physics B 644 21 (2002)
  191. Konopelchenko B G, Schief W K J. Phys. A: Math. Gen. 35 6125 (2002)
  192. Kanzieper E Phys. Rev. Lett. 89 (25) (2002)
  193. Mironov A, Morozov A Physics Letters B 524 217 (2002)
  194. Orlov A Yu, Scherbin D M Physica D: Nonlinear Phenomena 152-153 51 (2001)
  195. Braden H W, Mironov A, Morozov A Physics Letters B 514 293 (2001)
  196. GERASIMOV A, MOROZOV A, SELIVANOV K Int. J. Mod. Phys. A 16 1531 (2001)
  197. Paniak L D, Szabo R J Nuclear Physics B 593 671 (2001)
  198. Чехов Л О, Chekhov L O ТМФ 127 179 (2001)
  199. NISSIMOV E, PACHEVA S Int. J. Mod. Phys. A 16 2311 (2001)
  200. Горский А С, Gorsky A S ТМФ 125 3 (2000)
  201. Morozov A Particles and Fields Chapter 5 (1999) p. 127
  202. Kakei S J. Phys. Soc. Jpn. 68 2875 (1999)
  203. Konopelchenko B, Alonso L M Physics Letters A 258 272 (1999)
  204. Akhmedov E T Physics Letters B 442 152 (1998)
  205. Zarembo K L, Makeenko Yu M Uspekhi Fizicheskikh Nauk 168 3 (1998)
  206. Миронов А Д, Mironov A D ТМФ 114 163 (1998) [Mironov A D Theor Math Phys 114 127 (1998)]
  207. Aratyn H, Nissimov E, Pacheva S Physics Letters A 244 245 (1998)
  208. Gorsky A, Marshakov A et al Nuclear Physics B 527 690 (1998)
  209. Itoyama H, Morozov A Nuclear Physics B 491 529 (1997)
  210. Yoltukhovskii M V Neurophysiology 29 137 (1997)
  211. Aratyn H, Nissimov E, Pacheva S Physics Letters A 228 164 (1997)
  212. Винтерниц П, Winternitz P и др ТМФ 113 231 (1997)
  213. Matone M Journal of Geometry and Physics 21 381 (1997)
  214. Orlov A Yu, Winternitz P Theor Math Phys 113 1393 (1997)
  215. Orlov A Yu, Winternitz P 38 4644 (1997)
  216. Semenoff G W, Szabo R J Theor Math Phys 104 823 (1995)
  217. Juriev D V Journal of Geometry and Physics 16 275 (1995)

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