Выпуски

 / 

1994

 / 

Январь

  

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.

Текст pdf (2,5 Мб)
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)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

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 (226) ↓ Похожие статьи (20)

  1. Mishnyakov V, Morozov A, Reva M Nuclear Physics B 1010 116746 (2025)
  2. Kazakov V, Murali H, Vieira P J. High Energ. Phys. 2025 (9) (2025)
  3. Morozov A, Sleptsov A Eur. Phys. J. C 85 (10) (2025)
  4. Li Ch, Mironov A, Orlov A Yu Physics Letters B 860 139170 (2025)
  5. Azheev B, Tselousov N Nuclear Physics B 1018 116975 (2025)
  6. Morozov A Encyclopedia of Mathematical Physics (2025) p. 168
  7. Mishnyakov V, Morozov A, Reva M Physics Letters B 864 139417 (2025)
  8. Morozov A, Sifat H Eur. Phys. J. C 85 (6) (2025)
  9. Mironov A, Morozov A, Popolitov A Physics Letters B 869 139840 (2025)
  10. Yang D Journal of Mathematical Physics 66 (3) (2025)
  11. Mishnyakov V, Morozov A et al Int. J. Mod. Phys. A 40 (07) (2025)
  12. Galakhov D, Morozov A J. High Energ. Phys. 2025 (5) (2025)
  13. Morozov A, Oreshina A Physics Letters B 857 139006 (2024)
  14. Eynard B, Garcia-Failde E et al Ann. Henri Poincaré (2024)
  15. Mironov A, Morozov A, Popolitov A Phys. Rev. D 110 (12) (2024)
  16. Galakhov D, Morozov A, Tselousov N Phys. Rev. D 109 (6) (2024)
  17. Kubo N, Nosaka T J. High Energ. Phys. 2024 (7) (2024)
  18. Mironov A, Oreshina A, Popolitov A Eur. Phys. J. C 84 (7) (2024)
  19. Drachov Ya, Mironov A, Popolitov A Physics Letters B 849 138426 (2024)
  20. Mironov A, Morozov A et al Phys. Rev. D 110 (4) (2024)
  21. Mironov A, Mishnyakov V, Morozov A Nuclear Physics B 1001 116504 (2024)
  22. Wang G J. High Energ. Phys. 2023 (3) (2023)
  23. Vleeshouwers W L, Gritsev V J. Phys. A: Math. Theor. 56 (18) 185002 (2023)
  24. Mironov A, Mishnyakov V et al Eur. Phys. J. C 83 (5) (2023)
  25. Mishnyakov V, Morozov A, Suprun P Nuclear Physics B 992 116245 (2023)
  26. Drachov Ya, Zhabin A Eur. Phys. J. C 83 (5) (2023)
  27. Barseghyan S, Popolitov A Annals of Physics 449 169207 (2023)
  28. Mironov A, Morozov A J. High Energ. Phys. 2023 (3) (2023)
  29. Liu F, Mironov A et al Nuclear Physics B 993 116283 (2023)
  30. Na W, Yang B et al Adv. Appl. Clifford Algebras 33 (1) (2023)
  31. Morozov A, Tselousov N J. High Energ. Phys. 2023 (11) (2023)
  32. Morozov A Eur. Phys. J. C 83 (3) (2023)
  33. Wang N Reports on Mathematical Physics 91 (1) 79 (2023)
  34. Wang N Journal of Mathematical Physics 63 (12) (2022)
  35. Mironov A, Morozov A, Popolitov A Physics Letters B 828 137038 (2022)
  36. Wang N, Wu K Journal of Mathematical Physics 63 (2) (2022)
  37. Mironov A, Morozov A, Zakirova Z Physics Letters B 831 137178 (2022)
  38. Mishnyakov V, Suprun P Jetp Lett. 115 (8) 477 (2022)
  39. Mironov A, Mishnyakov V et al Physics Letters B 829 137041 (2022)
  40. Balthazar B, Giveon A et al J. High Energ. Phys. 2022 (1) (2022)
  41. Cui Zh, Bai Ya et al Nuclear Physics B 984 115986 (2022)
  42. Wang N, Wu K Nuclear Physics B 974 115642 (2022)
  43. Khlaif O, Kimura T J. High Energ. Phys. 2022 (4) (2022)
  44. Mironov A, Morozov A, Popolitov A Physics Letters B 824 136833 (2022)
  45. Mironov A, Morozov A Physics Letters B 835 137573 (2022)
  46. Wang R, Zhang Ch-H et al Nuclear Physics B 985 115989 (2022)
  47. Mishnyakov V, Oreshina A Eur. Phys. J. C 82 (6) (2022)
  48. Lanina E, Morozov A Eur. Phys. J. C 82 (11) (2022)
  49. Mironov A, Mishnyakov V et al Nuclear Physics B 985 116022 (2022)
  50. Mironov A, Morozov A Phys. Rev. D 106 (12) (2022)
  51. Mironov A, Morozov A J. High Energ. Phys. 2021 (2) (2021)
  52. Mironov A, Morozov A Eur. Phys. J. C 81 (3) (2021)
  53. Morozov A J. High Energ. Phys. 2021 (10) (2021)
  54. Araujo T Nuclear Physics B 972 115566 (2021)
  55. Mironov A, Morozov A Physics Letters B 816 136196 (2021)
  56. Mironov A, Mishnyakov V, Morozov A Physics Letters B 823 136721 (2021)
  57. Mironov A, Morozov A Physics Letters B 816 136268 (2021)
  58. Altland A, Sonner Ju SciPost Phys. 11 (2) (2021)
  59. Beccaria M, Hasan A J. High Energ. Phys. 2021 (4) (2021)
  60. Anokhina A S Phys. Part. Nuclei 52 (3) 374 (2021)
  61. Mironov A D, Morozov A et al Lett Math Phys 111 (5) (2021)
  62. Okuyama K, Sakai K J. High Energ. Phys. 2021 (9) (2021)
  63. Mironov A, Mishnyakov V et al Eur. Phys. J. C 81 (12) (2021)
  64. Mironov A D, Morozov A Physics Letters B 819 136474 (2021)
  65. Tian K, Li S et al Physics Letters B 822 136643 (2021)
  66. Beccaria M, Tseytlin A A J. High Energ. Phys. 2021 (1) (2021)
  67. Mironov A, Morozov A Physics Letters B 816 136221 (2021)
  68. Mironov A, Mishnyakov V et al Jetp Lett. 113 (11) 728 (2021)
  69. Cassia L, Lodin R, Zabzine M J. High Energ. Phys. 2020 (10) (2020)
  70. Orlov A Yu Geometric Methods in Physics XXXVIII Trends in Mathematics Chapter 15 (2020) p. 221
  71. Morozov A, Popolitov A, Shakirov Sh Physics Letters B 811 135932 (2020)
  72. Anokhina A S Phys. Part. Nuclei 51 (2) 172 (2020)
  73. Dubrovin B, Liu S-Q et al Commun. Math. Phys. 379 (2) 461 (2020)
  74. Morozov A, Tselousov N Eur. Phys. J. C 80 (12) (2020)
  75. Lodin R, Popolitov A et al Lett Math Phys 110 (1) 179 (2020)
  76. Nieri F, Pan Y, Zabzine M Commun. Math. Phys. 366 (1) 397 (2019)
  77. Li Ch-X, Qin Zh-Yu, Shen Sh-F J. Phys. Soc. Jpn. 88 (12) 124003 (2019)
  78. Cassia L, Lodin R et al J. High Energ. Phys. 2019 (12) (2019)
  79. Itoyama H, Mironov A, Morozov A Physics Letters B 788 76 (2019)
  80. Morozov A Eur. Phys. J. C 79 (1) (2019)
  81. Morozov A Physics Letters B 792 205 (2019)
  82. Mironov A, Morozov A, Zakirova Z J. High Energ. Phys. 2019 (10) (2019)
  83. Mironov A, Morozov A Physics Letters B 785 207 (2018)
  84. Morozov A Physics Letters B 785 175 (2018)
  85. Mironov A, Morozov A J. High Energ. Phys. 2018 (8) (2018)
  86. Nieri F, Pan Y et al EPJ Web Conf. 191 06005 (2018)
  87. Itoyama H, Mironov A, Morozov A Nuclear Physics B 932 52 (2018)
  88. Ivanitskii G R Phys.-Usp. 61 (9) 871 (2018)
  89. Morozov A, Popolitov A, Shakirov Sh Physics Letters B 784 342 (2018)
  90. Betzios P, Gürsoy U, Papadoulaki O Nuclear Physics B 928 356 (2018)
  91. van de Leur J W, Orlov A Yu J. Phys. A: Math. Theor. 51 (2) 025208 (2018)
  92. Mironov A, Morozov A Physics Letters B 774 210 (2017)
  93. Ivanitskii G R Успехи физических наук 187 (07) 757 (2017) [Ivanitskii G R Phys.-Usp. 60 (7) 705 (2017)]
  94. Itoyama H, Mironov A, Morozov A J. High Energ. Phys. 2017 (6) (2017)
  95. Itoyama H, Mironov A, Morozov A Physics Letters B 771 180 (2017)
  96. Mironov A, Morozov A Physics Letters B 771 503 (2017)
  97. Nedelin A, Nieri F, Zabzine M Commun. Math. Phys. 353 (3) 1059 (2017)
  98. Nedelin A, Zabzine M J. High Energ. Phys. 2017 (3) (2017)
  99. Popolitov A Jetp Lett. 103 (2) 137 (2016)
  100. Morozov A, Zenkevich Y J. High Energ. Phys. 2016 (2) (2016)
  101. Procházka Tomáš J. High Energ. Phys. 2016 (10) (2016)
  102. Morozov A A Phys. Part. Nuclei 47 (5) 775 (2016)
  103. Ding X-M, Li Yu, Meng L J. High Energ. Phys. 2016 (1) (2016)
  104. Mironov A, Morozov A, Zenkevich Y Physics Letters B 762 196 (2016)
  105. Natanzon S M, Zabrodin A V J. Phys. A: Math. Theor. 49 (14) 145206 (2016)
  106. Lafortune S, Li Ch-X J. Phys. A: Math. Theor. 49 (47) 475202 (2016)
  107. Awata H, Kanno H et al J. High Energ. Phys. 2016 (7) (2016)
  108. Melnikov D, Mironov A, Morozov A J. High Energ. Phys. 2016 (5) (2016)
  109. Mironov A, Morozov A et al Int. J. Mod. Phys. A 30 (26) 1550169 (2015)
  110. Alexandrov A J. High Energ. Phys. 2015 (3) (2015)
  111. Kanning N, Ko Yu, Staudacher M Nuclear Physics B 894 407 (2015)
  112. Kanzieper E Constr Approx 41 (3) 615 (2015)
  113. Morozov A, Morozov A, Popolitov A Physics Letters B 749 309 (2015)
  114. Itoyama H, Yoshioka R Prog. Theor. Exp. Phys. 2015 (11) 11B103 (2015)
  115. Kimura T Progress of Theoretical and Experimental Physics 2014 (12) 123A01 (2014)
  116. Orlov A Yu Physics Letters A 378 (4) 319 (2014)
  117. Alexandrov A, Leurent S et al Nuclear Physics B 883 173 (2014)
  118. Alexandrov A Lett Math Phys 104 (1) 75 (2014)
  119. Kimura T Progress of Theoretical and Experimental Physics 2014 (10) 103B04 (2014)
  120. Alexandrov A, Mironov A et al Jetp Lett. 100 (4) 271 (2014)
  121. Alexandrov A, Mironov A et al J. High Energ. Phys. 2014 (11) (2014)
  122. Li M, Li Ch et al Journal of Mathematical Physics 54 (4) (2013)
  123. Alexandrov A, Zabrodin A Journal of Geometry and Physics 67 37 (2013)
  124. Mironov A, Morozov A, Sleptsov A Eur. Phys. J. C 73 (7) (2013)
  125. Mironov A, Morozov A, Natanzon S Journal of Geometry and Physics 62 (2) 148 (2012)
  126. Морозов А Ю, Morozov A Yu Теоретическая и математическая физика 173 (1) 104 (2012)
  127. Mironov A, Morozov A, Zakirova Z Physics Letters B 711 (3-4) 332 (2012)
  128. Takasaki K, Takebe T Anal.Math.Phys. 2 (2) 171 (2012)
  129. MIRONOV A, MOROZOV A, SHAKIROV SH Int. J. Mod. Phys. A 27 (01) 1230001 (2012)
  130. Галахов Д В, Galakhov D V и др ТМФ 172 (1) 73 (2012)
  131. Itoyama H, Mironov A et al J. High Energ. Phys. 2012 (7) (2012)
  132. Alexandrov A, Mironov A et al J. Phys. A: Math. Theor. 45 (4) 045209 (2012)
  133. Alexandrov A J. Phys.: Conf. Ser. 343 012009 (2012)
  134. Shakirov Sh Physics Letters A 375 (6) 984 (2011)
  135. Миронов А Д, Mironov A D и др ТМФ 166 (1) 3 (2011) [Mironov A D, Morozov A Yu, Natanzon S M Theor Math Phys 166 (1) 1 (2011)]
  136. Morozov A, Shakirov Sh Journal of Geometry and Physics 61 (3) 708 (2011)
  137. ALEXANDROV A Mod. Phys. Lett. A 26 (29) 2193 (2011)
  138. Alexandrov A Nuclear Physics B 851 (3) 620 (2011)
  139. Mironov A, Morozov A, Morozov A Nuclear Physics B 843 (2) 534 (2011)
  140. Tian KeLei, He JingSong et al Sci. China Math. 54 (2) 257 (2011)
  141. Brown T W Phys. Rev. D 83 (8) (2011)
  142. Mironov A, Morozov A, Shakirov Sh J. High Energ. Phys. 2011 (2) (2011)
  143. Mironov A, Morozov A, Shakirov Sh J. High Energ. Phys. 2011 (3) (2011)
  144. Tian K, Hea J et al Chin. Ann. Math. Ser. B 32 (6) 895 (2011)
  145. Mironov A, Morozov A, Shakirov Sh J. High Energ. Phys. 2010 (2) (2010)
  146. Osipov V A, Kanzieper E Annals of Physics 325 (10) 2251 (2010)
  147. Mironov A, Mironov S et al J. Phys. A: Math. Theor. 43 (5) 055402 (2010)
  148. Морозов А Ю, Morozov A Yu ТМФ 162 (1) 3 (2010) [Morozov A Yu Theor Math Phys 162 (1) 1 (2010)]
  149. MIRONOV A, MOROZOV A, SHAKIROV SH Int. J. Mod. Phys. A 25 (16) 3173 (2010)
  150. Mironov A, Morozov A J. High Energ. Phys. 2010 (4) (2010)
  151. Mironov A, Morozov A J. Phys. A: Math. Theor. 43 (19) 195401 (2010)
  152. ALEXANDROV A, MIRONOV A et al Int. J. Mod. Phys. A 24 (27) 4939 (2009)
  153. Galakhov D, Itoyama H et al Nuclear Physics B 823 (3) 289 (2009)
  154. Dimakis A, Müller-Hoissen F Generalized Lie Theory in Mathematics, Physics and Beyond Chapter 2 (2009) p. 9
  155. Morozov A, Shakirov Sh J. High Energy Phys. 2009 (12) 003 (2009)
  156. MOROZOV A, SHAKIROV SH Mod. Phys. Lett. A 24 (33) 2659 (2009)
  157. Morozov A, Shakirov Sh J. High Energy Phys. 2009 (04) 064 (2009)
  158. Wang D Journal of Mathematical Physics 50 (7) (2009)
  159. Morozov A, Shakirov Sh J. High Energy Phys. 2009 (12) 002 (2009)
  160. Mironov A, Morozov A Physics Letters B 680 (2) 188 (2009)
  161. Osipov V A, Kanzieper E J. Phys. A: Math. Theor. 42 (47) 475101 (2009)
  162. Akhmedov E T Phys. Atom. Nuclei 72 (9) 1574 (2009)
  163. Mironov A, Morozov A J. High Energy Phys. 2009 (02) 024 (2009)
  164. Alexandrov A, Mironov A, Morozov A J. High Energy Phys. 2009 (12) 053 (2009)
  165. DOLOTIN V, MOROZOV A Int. J. Mod. Phys. A 23 (22) 3613 (2008)
  166. Morozov A J. High Energy Phys. 2008 (05) 086 (2008)
  167. Морозов А Ю, Morozov A Yu ТМФ 157 (2) 208 (2008) [Morozov A Yu Theor Math Phys 157 (2) 1542 (2008)]
  168. Okuyama K Physics Letters B 645 (2-3) 275 (2007)
  169. Alexandrov A, Mironov A, Morozov A Physica D: Nonlinear Phenomena 235 (1-2) 126 (2007)
  170. Kostov I K, Petkova V B Nuclear Physics B 769 (3) 175 (2007)
  171. Александров А С, Alexandrov A S и др ТМФ 150 (2) 179 (2007) [Alexandrov A S, Mironov A D, Morozov A Yu Theor Math Phys 150 (2) 153 (2007)]
  172. Ellwood I, Hashimoto A J. High Energy Phys. 2006 (02) 002 (2006)
  173. ALEXANDROV A, MIRONOV A, MOROZOV A Int. J. Mod. Phys. A 21 (12) 2481 (2006)
  174. 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
  175. Чехов Л О, Chekhov L O и др УМН 61 (3) 93 (2006)
  176. Chekhov L J. Phys. A: Math. Gen. 39 (28) 8857 (2006)
  177. Александров А С, Alexandrov A S и др ТМФ 142 (3) 419 (2005) [Alexandrov A S, Mironov A D, Morozov A Yu Theor Math Phys 142 (3) 349 (2005)]
  178. 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
  179. Orlov A Yu Acta Appl Math 86 (1-2) 131 (2005)
  180. Okuyama K J. High Energy Phys. 2005 (04) 002 (2005)
  181. Sedrakyan T A Nuclear Physics B 729 (3) 526 (2005)
  182. Klemm A Fortschritte der Physik 53 (7-8) 720 (2005)
  183. YU ORLOV A Int. J. Mod. Phys. A 19 (supp02) 276 (2004)
  184. Konopelchenko B G, Moro A J. Phys. A: Math. Gen. 37 (10) L105 (2004)
  185. Chiantese S, Klemm A, Runkel I J. High Energy Phys. 2004 (03) 033 (2004)
  186. JURČO BRANISLAV Mod. Phys. Lett. A 19 (22) 1661 (2004)
  187. ALEXANDROV A, MOROZOV A, MIRONOV A Int. J. Mod. Phys. A 19 (24) 4127 (2004)
  188. Maldacena Ju, Moore G et al J. High Energy Phys. 2004 (10) 020 (2004)
  189. Миронов А Д, Mironov A D и др ТМФ 135 (3) 434 (2003)
  190. Fyodorov Ya V, Strahov E J. Phys. A: Math. Gen. 36 (12) 3203 (2003)
  191. Itoyama H, Morozov A Nuclear Physics B 657 53 (2003)
  192. Zinn-Justin P, Zuber J-B J. Phys. A: Math. Gen. 36 (12) 3173 (2003)
  193. Morozov A, Niemi A J Nuclear Physics B 666 (3) 311 (2003)
  194. Dymarsky A, Pestun V Phys. Rev. D 67 (12) (2003)
  195. Konopelchenko B, Moro A J. Phys. A: Math. Gen. 36 (47) 11837 (2003)
  196. Gorbunov I V, Sharapov A A Physics Letters B 531 (3-4) 255 (2002)
  197. Marshakov A V Uspekhi Fizicheskikh Nauk 172 (9) 977 (2002)
  198. Dijkgraaf R, Vafa C Nuclear Physics B 644 (1-2) 21 (2002)
  199. Mironov A, Morozov A Physics Letters B 524 (1-2) 217 (2002)
  200. Kanzieper E Phys. Rev. Lett. 89 (25) (2002)
  201. Konopelchenko B G, Schief W K J. Phys. A: Math. Gen. 35 (29) 6125 (2002)
  202. Orlov A Yu, Scherbin D M Physica D: Nonlinear Phenomena 152-153 51 (2001)
  203. Chekhov L O Theoretical and Mathematical Physics 127 (2) 557 (2001) [Чехов Л О, Chekhov L O ТМФ 127 (2) 179 (2001)]
  204. Braden H W, Mironov A, Morozov A Physics Letters B 514 (3-4) 293 (2001)
  205. Paniak L D, Szabo R J Nuclear Physics B 593 (3) 671 (2001)
  206. NISSIMOV E, PACHEVA S Int. J. Mod. Phys. A 16 (13) 2311 (2001)
  207. GERASIMOV A, MOROZOV A, SELIVANOV K Int. J. Mod. Phys. A 16 (09) 1531 (2001)
  208. Горский А С, Gorsky A S ТМФ 125 (1) 3 (2000)
  209. Morozov A Particles and Fields Chapter 5 (1999) p. 127
  210. Kakei S J. Phys. Soc. Jpn. 68 (9) 2875 (1999)
  211. Konopelchenko B, Alonso L M Physics Letters A 258 (4-6) 272 (1999)
  212. Aratyn H, Nissimov E, Pacheva S Physics Letters A 244 (4) 245 (1998)
  213. Gorsky A, Marshakov A et al Nuclear Physics B 527 (3) 690 (1998)
  214. Akhmedov E T Physics Letters B 442 (1-4) 152 (1998)
  215. Миронов А Д, Mironov A D ТМФ 114 (2) 163 (1998) [Mironov A D Theor Math Phys 114 (2) 127 (1998)]
  216. Zarembo K L, Makeenko Yu M Uspekhi Fizicheskikh Nauk 168 (1) 3 (1998)
  217. Orlov A Yu, Winternitz P Journal of Mathematical Physics 38 (9) 4644 (1997)
  218. Chekhov L Acta Applicandae Mathematicae 48 (1) 33 (1997)
  219. Aratyn H, Nissimov E, Pacheva S Physics Letters A 228 (3) 164 (1997)
  220. Orlov A Yu, Winternitz P Theor Math Phys 113 (2) 1393 (1997)
  221. Matone M Journal of Geometry and Physics 21 (4) 381 (1997)
  222. Yoltukhovskii M V Neurophysiology 29 (3) 137 (1997)
  223. Itoyama H, Morozov A Nuclear Physics B 491 (3) 529 (1997)
  224. Винтерниц П, Winternitz P и др ТМФ 113 (2) 231 (1997)
  225. Juriev D V Journal of Geometry and Physics 16 (3) 275 (1995)
  226. Semenoff G W, Szabo R J Theor Math Phys 104 (1) 823 (1995)

© Успехи физических наук, 1918–2025
Электронная почта: ufn@ufn.ru Телефоны и адреса редакции О журнале Пользовательское соглашение