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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 (213) ↓ Похожие статьи (20)

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

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