RSS feeds
ÐóññêèéEnglish
Issue 12, 2024
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

1994

 / 

January

←  →

Reviews of topical problems


Integrability and matrix models


Russian Federation State Scientific Center ‘A.I. Alikhanov Institute of Theoretical and Experimental Physics’, ul. Bolshaya Cheremushkinskaya 25, Moscow, 117259, Russian Federation

The theory of matrix models is reviewed from the point of view of its relation to integrable hierarchies. Discrete 1-matrix, 2-matrix, ’conformal’ (multicomponent) and Kontsevich models are considered in some detail, together with the Ward identites (’W-constraints’), determinantal formulas and continuum limits, taking one kind of model into another. Subtle points and directions of the future research are also discussed.

Fulltext pdf (1.5 MB)
Fulltext is also available at DOI: 10.1070/PU1994v037n01ABEH000001
PACS: 02.10.+b, 11.17.+y
DOI: 10.1070/PU1994v037n01ABEH000001
URL: https://ufn.ru/en/articles/1994/1/a/
A1994NA86300001
Citation: Morozov A Yu "Integrability and matrix models" Phys. Usp. 37 1–55 (1994)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Îðèãèíàë: Ìîðîçîâ À Þ «Èíòåãðèðóåìîñòü è ìàòðè÷íûå ìîäåëè» ÓÔÍ 164 3–62 (1994); DOI: 10.3367/UFNr.0164.199401a.0003

References (113) Cited by (215) ↓ Similar articles (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. Galakhov D, Morozov A, Tselousov N Phys. Rev. D 109 (6) (2024)
  6. Mironov A, Oreshina A, Popolitov A Eur. Phys. J. C 84 (7) (2024)
  7. Eynard B, Garcia-Failde E et al Ann. Henri Poincaré (2024)
  8. Mironov A, Morozov A et al Phys. Rev. D 110 (4) (2024)
  9. Morozov A, Oreshina A Physics Letters B 857 139006 (2024)
  10. Kubo N, Nosaka T J. High Energ. Phys. 2024 (7) (2024)
  11. Mironov A, Mishnyakov V, Morozov A Nuclear Physics B 1001 116504 (2024)
  12. Vleeshouwers W L, Gritsev V J. Phys. A: Math. Theor. 56 185002 (2023)
  13. Morozov A, Tselousov N J. High Energ. Phys. 2023 (11) (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. Drachov Ya, Zhabin A Eur. Phys. J. C 83 (5) (2023)
  18. Mironov A, Morozov A J. High Energ. Phys. 2023 (3) (2023)
  19. Barseghyan S, Popolitov A Annals Of Physics 449 169207 (2023)
  20. Morozov A Eur. Phys. J. C 83 (3) (2023)
  21. Mishnyakov V, Morozov A, Suprun P Nuclear Physics B 992 116245 (2023)
  22. Na W, Yang B et al Adv. Appl. Clifford Algebras 33 (1) (2023)
  23. Mironov A, Mishnyakov V et al Eur. Phys. J. C 83 (5) (2023)
  24. Mironov A, Morozov A, Zakirova Z Physics Letters B 831 137178 (2022)
  25. Wang N 63 (12) (2022)
  26. Khlaif O, Kimura T J. High Energ. Phys. 2022 (4) (2022)
  27. Mishnyakov V, Oreshina A Eur. Phys. J. C 82 (6) (2022)
  28. Balthazar B, Giveon A et al J. High Energ. Phys. 2022 (1) (2022)
  29. Mishnyakov V, Suprun P Jetp Lett. 115 477 (2022)
  30. Mironov A, Morozov A Physics Letters B 835 137573 (2022)
  31. Wang R, Zhang Ch-H et al Nuclear Physics B 985 115989 (2022)
  32. Mironov A, Morozov A, Popolitov A Physics Letters B 828 137038 (2022)
  33. Mironov A, Morozov A Phys. Rev. D 106 (12) (2022)
  34. Wang N, Wu K 63 (2) (2022)
  35. Mironov A, Morozov A, Popolitov A Physics Letters B 824 136833 (2022)
  36. Mironov A, Mishnyakov V et al Physics Letters B 829 137041 (2022)
  37. Mironov A, Mishnyakov V et al Nuclear Physics B 985 116022 (2022)
  38. Cui Zh, Bai Ya et al Nuclear Physics B 984 115986 (2022)
  39. Lanina E, Morozov A Eur. Phys. J. C 82 (11) (2022)
  40. Wang N, Wu K Nuclear Physics B 974 115642 (2022)
  41. Mironov A, Morozov A Physics Letters B 816 136196 (2021)
  42. Morozov A J. High Energ. Phys. 2021 (10) (2021)
  43. Okuyama K, Sakai K J. High Energ. Phys. 2021 (9) (2021)
  44. Mironov A, Morozov A J. High Energ. Phys. 2021 (2) (2021)
  45. Anokhina A S Phys. Part. Nuclei 52 374 (2021)
  46. Mironov A D, Morozov A et al Lett Math Phys 111 (5) (2021)
  47. Tian K, Li S et al Physics Letters B 822 136643 (2021)
  48. Beccaria M, Tseytlin A A J. High Energ. Phys. 2021 (1) (2021)
  49. Mironov A, Mishnyakov V et al Jetp Lett. 113 728 (2021)
  50. Altland A, Sonner Ju SciPost Phys. 11 (2) (2021)
  51. Mironov A, Morozov A Physics Letters B 816 136221 (2021)
  52. Beccaria M, Hasan A J. High Energ. Phys. 2021 (4) (2021)
  53. Mironov A, Mishnyakov V et al Eur. Phys. J. C 81 (12) (2021)
  54. Mironov A, Morozov A Eur. Phys. J. C 81 (3) (2021)
  55. Araujo T Nuclear Physics B 972 115566 (2021)
  56. Mironov A, Morozov A Physics Letters B 816 136268 (2021)
  57. Mironov A D, Morozov A Physics Letters B 819 136474 (2021)
  58. Mironov A, Mishnyakov V, Morozov A Physics Letters B 823 136721 (2021)
  59. Anokhina A S Phys. Part. Nuclei 51 172 (2020)
  60. Dubrovin B, Liu S-Q et al Commun. Math. Phys. 379 461 (2020)
  61. Orlov A Yu Geometric Methods in Physics XXXVIII Trends In Mathematics Chapter 15 (2020) p. 221
  62. Lodin R, Popolitov A et al Lett Math Phys 110 179 (2020)
  63. Cassia L, Lodin R, Zabzine M J. High Energ. Phys. 2020 (10) (2020)
  64. Morozov A, Tselousov N Eur. Phys. J. C 80 (12) (2020)
  65. Morozov A, Popolitov A, Shakirov Sh Physics Letters B 811 135932 (2020)
  66. Morozov A Physics Letters B 792 205 (2019)
  67. Nieri F, Pan Y, Zabzine M Commun. Math. Phys. 366 397 (2019)
  68. Cassia L, Lodin R et al J. High Energ. Phys. 2019 (12) (2019)
  69. Mironov A, Morozov A, Zakirova Z J. High Energ. Phys. 2019 (10) (2019)
  70. Li Ch-X, Qin Zh-Yu, Shen Sh-F J. Phys. Soc. Jpn. 88 124003 (2019)
  71. Morozov A Eur. Phys. J. C 79 (1) (2019)
  72. Itoyama H, Mironov A, Morozov A Physics Letters B 788 76 (2019)
  73. Morozov A, Popolitov A, Shakirov Sh Physics Letters B 784 342 (2018)
  74. van de Leur J W, Orlov A Yu J. Phys. A: Math. Theor. 51 025208 (2018)
  75. Morozov A Physics Letters B 785 175 (2018)
  76. Mironov A, Morozov A Physics Letters B 785 207 (2018)
  77. Nieri F, Pan Y et al EPJ Web Conf. 191 06005 (2018)
  78. Betzios P, Gürsoy U, Papadoulaki O Nuclear Physics B 928 356 (2018)
  79. Ivanitskii G R Phys.-Usp. 61 871 (2018)
  80. Itoyama H, Mironov A, Morozov A Nuclear Physics B 932 52 (2018)
  81. Mironov A, Morozov A J. High Energ. Phys. 2018 (8) (2018)
  82. Ivanitskii G R Uspekhi Fizicheskikh Nauk 187 757 (2017) [Ivanitskii G R Phys.-Usp. 60 705 (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. Nedelin A, Nieri F, Zabzine M Commun. Math. Phys. 353 1059 (2017)
  87. Itoyama H, Mironov A, Morozov A Physics Letters B 771 180 (2017)
  88. Mironov A, Morozov A Physics Letters B 774 210 (2017)
  89. Lafortune S, Li Ch-X J. Phys. A: Math. Theor. 49 475202 (2016)
  90. Mironov A, Morozov A, Zenkevich Y Physics Letters B 762 196 (2016)
  91. Ding X-M, Li Yu, Meng L J. High Energ. Phys. 2016 (1) (2016)
  92. Procházka Tomáš J. High Energ. Phys. 2016 (10) (2016)
  93. Popolitov A Jetp Lett. 103 137 (2016)
  94. Melnikov D, Mironov A, Morozov A J. High Energ. Phys. 2016 (5) (2016)
  95. Natanzon S M, Zabrodin A V J. Phys. A: Math. Theor. 49 145206 (2016)
  96. Morozov A A Phys. Part. Nuclei 47 775 (2016)
  97. Awata H, Kanno H et al J. High Energ. Phys. 2016 (7) (2016)
  98. Morozov A, Zenkevich Y J. High Energ. Phys. 2016 (2) (2016)
  99. Mironov A, Morozov A et al Int. J. Mod. Phys. A 30 1550169 (2015)
  100. Itoyama H, Yoshioka R Prog. Theor. Exp. Phys. 2015 11B103 (2015)
  101. Kanzieper E Constr Approx 41 615 (2015)
  102. Kanning N, Ko Yu, Staudacher M Nuclear Physics B 894 407 (2015)
  103. Morozov A, Morozov A, Popolitov A Physics Letters B 749 309 (2015)
  104. Alexandrov A J. High Energ. Phys. 2015 (3) (2015)
  105. Alexandrov A, Mironov A et al J. High Energ. Phys. 2014 (11) (2014)
  106. Kimura T Progress Of Theoretical And Experimental Physics 2014 103B04 (2014)
  107. Alexandrov A Lett Math Phys 104 75 (2014)
  108. Alexandrov A, Leurent S et al Nuclear Physics B 883 173 (2014)
  109. Kimura T Progress Of Theoretical And Experimental Physics 2014 123A01 (2014)
  110. Alexandrov A, Mironov A et al Jetp Lett. 100 271 (2014)
  111. Orlov A Yu Physics Letters A 378 319 (2014)
  112. Li M, Li Ch et al 54 (4) (2013)
  113. Mironov A, Morozov A, Sleptsov A Eur. Phys. J. C 73 (7) (2013)
  114. Alexandrov A, Zabrodin A Journal Of Geometry And Physics 67 37 (2013)
  115. Takasaki K, Takebe T Anal.Math.Phys. 2 171 (2012)
  116. MIRONOV A, MOROZOV A, SHAKIROV SH Int. J. Mod. Phys. A 27 1230001 (2012)
  117. Alexandrov A J. Phys.: Conf. Ser. 343 012009 (2012)
  118. Alexandrov A, Mironov A et al J. Phys. A: Math. Theor. 45 045209 (2012)
  119. Itoyama H, Mironov A et al J. High Energ. Phys. 2012 (7) (2012)
  120. Morozov A Yu, Morozov A Yu Teoreticheskaya Matematicheskaya Fizika 173 104 (2012)
  121. Mironov A, Morozov A, Zakirova Z Physics Letters B 711 332 (2012)
  122. Galakhov D V, Galakhov D V i dr Teor. Mat. Fiz. 172 73 (2012)
  123. Mironov A, Morozov A, Natanzon S Journal Of Geometry And Physics 62 148 (2012)
  124. ALEXANDROV A Mod. Phys. Lett. A 26 2193 (2011)
  125. Mironov A D, Mironov A D i dr Teor. Mat. Fiz. 166 3 (2011) [Mironov A D, Morozov A Yu, Natanzon S M Theor Math Phys 166 1 (2011)]
  126. Morozov A, Shakirov Sh Journal Of Geometry And Physics 61 708 (2011)
  127. Mironov A, Morozov A, Morozov A Nuclear Physics B 843 534 (2011)
  128. Brown T W Phys. Rev. D 83 (8) (2011)
  129. Alexandrov A Nuclear Physics B 851 620 (2011)
  130. Tian KeLei, He JingSong et al Sci. China Math. 54 257 (2011)
  131. Mironov A, Morozov A, Shakirov Sh J. High Energ. Phys. 2011 (2) (2011)
  132. Mironov A, Morozov A, Shakirov Sh J. High Energ. Phys. 2011 (3) (2011)
  133. Tian K, Hea J et al Chin. Ann. Math. Ser. B 32 895 (2011)
  134. Shakirov Sh Physics Letters A 375 984 (2011)
  135. Osipov V A, Kanzieper E Annals Of Physics 325 2251 (2010)
  136. Mironov A, Morozov A J. Phys. A: Math. Theor. 43 195401 (2010)
  137. Mironov A, Mironov S et al J. Phys. A: Math. Theor. 43 055402 (2010)
  138. MIRONOV A, MOROZOV A, SHAKIROV SH Int. J. Mod. Phys. A 25 3173 (2010)
  139. Mironov A, Morozov A, Shakirov Sh J. High Energ. Phys. 2010 (2) (2010)
  140. Morozov A Yu, Morozov A Yu Teor. Mat. Fiz. 162 3 (2010) [Morozov A Yu Theor Math Phys 162 1 (2010)]
  141. Mironov A, Morozov A J. High Energ. Phys. 2010 (4) (2010)
  142. Wang D 50 (7) (2009)
  143. MOROZOV A, SHAKIROV SH Mod. Phys. Lett. A 24 2659 (2009)
  144. Dimakis A, Müller-Hoissen F Generalized Lie Theory in Mathematics, Physics and Beyond Chapter 2 (2009) p. 9
  145. Mironov A, Morozov A J. High Energy Phys. 2009 024 (2009)
  146. Osipov V A, Kanzieper E J. Phys. A: Math. Theor. 42 475101 (2009)
  147. Mironov A, Morozov A Physics Letters B 680 188 (2009)
  148. Morozov A, Shakirov Sh J. High Energy Phys. 2009 002 (2009)
  149. Akhmedov E T Phys. Atom. Nuclei 72 1574 (2009)
  150. ALEXANDROV A, MIRONOV A et al Int. J. Mod. Phys. A 24 4939 (2009)
  151. Morozov A, Shakirov Sh J. High Energy Phys. 2009 064 (2009)
  152. Morozov A, Shakirov Sh J. High Energy Phys. 2009 003 (2009)
  153. Galakhov D, Itoyama H et al Nuclear Physics B 823 289 (2009)
  154. Alexandrov A, Mironov A, Morozov A J. High Energy Phys. 2009 053 (2009)
  155. Morozov A Yu, Morozov A Yu Teor. Mat. Fiz. 157 208 (2008) [Morozov A Yu Theor Math Phys 157 1542 (2008)]
  156. DOLOTIN V, MOROZOV A Int. J. Mod. Phys. A 23 3613 (2008)
  157. Morozov A J. High Energy Phys. 2008 086 (2008)
  158. Okuyama K Physics Letters B 645 275 (2007)
  159. Alexandrov A, Mironov A, Morozov A Physica D: Nonlinear Phenomena 235 126 (2007)
  160. Aleksandrov A S, Alexandrov A S i dr Teor. Mat. Fiz. 150 179 (2007) [Alexandrov A S, Mironov A D, Morozov A Yu Theor Math Phys 150 153 (2007)]
  161. Kostov I K, Petkova V B Nuclear Physics B 769 175 (2007)
  162. 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
  163. Chekhov L J. Phys. A: Math. Gen. 39 8857 (2006)
  164. Ellwood I, Hashimoto A J. High Energy Phys. 2006 002 (2006)
  165. ALEXANDROV A, MIRONOV A, MOROZOV A Int. J. Mod. Phys. A 21 2481 (2006)
  166. Chekhov L O, Chekhov L O i dr Usp. Mat. Nauk 61 93 (2006)
  167. Orlov A Yu Acta Appl Math 86 131 (2005)
  168. 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
  169. Klemm A Fortschritte Der Physik 53 720 (2005)
  170. Aleksandrov A S, Alexandrov A S i dr Teor. Mat. Fiz. 142 419 (2005) [Alexandrov A S, Mironov A D, Morozov A Yu Theor Math Phys 142 349 (2005)]
  171. Sedrakyan T A Nuclear Physics B 729 526 (2005)
  172. Okuyama K J. High Energy Phys. 2005 002 (2005)
  173. ALEXANDROV A, MOROZOV A, MIRONOV A Int. J. Mod. Phys. A 19 4127 (2004)
  174. YU ORLOV A Int. J. Mod. Phys. A 19 276 (2004)
  175. JURČO BRANISLAV Mod. Phys. Lett. A 19 1661 (2004)
  176. Maldacena Ju, Moore G et al J. High Energy Phys. 2004 020 (2004)
  177. Konopelchenko B G, Moro A J. Phys. A: Math. Gen. 37 L105 (2004)
  178. Chiantese S, Klemm A, Runkel I J. High Energy Phys. 2004 033 (2004)
  179. Morozov A, Niemi A J Nuclear Physics B 666 311 (2003)
  180. Zinn-Justin P, Zuber J-B J. Phys. A: Math. Gen. 36 3173 (2003)
  181. Dymarsky A, Pestun V Phys. Rev. D 67 (12) (2003)
  182. Fyodorov Ya V, Strahov E J. Phys. A: Math. Gen. 36 3203 (2003)
  183. Mironov A D, Mironov A D i dr Teor. Mat. Fiz. 135 434 (2003)
  184. Itoyama H, Morozov A Nuclear Physics B 657 53 (2003)
  185. Konopelchenko B, Moro A J. Phys. A: Math. Gen. 36 11837 (2003)
  186. Mironov A, Morozov A Physics Letters B 524 217 (2002)
  187. Marshakov A V Uspekhi Fizicheskikh Nauk 172 977 (2002)
  188. Dijkgraaf R, Vafa C Nuclear Physics B 644 21 (2002)
  189. Gorbunov I V, Sharapov A A Physics Letters B 531 255 (2002)
  190. Kanzieper E Phys. Rev. Lett. 89 (25) (2002)
  191. Konopelchenko B G, Schief W K J. Phys. A: Math. Gen. 35 6125 (2002)
  192. NISSIMOV E, PACHEVA S Int. J. Mod. Phys. A 16 2311 (2001)
  193. Orlov A Yu, Scherbin D M Physica D: Nonlinear Phenomena 152-153 51 (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. Braden H W, Mironov A, Morozov A Physics Letters B 514 293 (2001)
  197. Chekhov L O, Chekhov L O Teor. Mat. Fiz. 127 179 (2001)
  198. Gorskii A S, Gorsky A S Teor. Mat. Fiz. 125 3 (2000)
  199. Konopelchenko B, Alonso L M Physics Letters A 258 272 (1999)
  200. Morozov A Particles and Fields Chapter 5 (1999) p. 127
  201. Kakei S J. Phys. Soc. Jpn. 68 2875 (1999)
  202. Mironov A D, Mironov A D Teor. Mat. Fiz. 114 163 (1998) [Mironov A D Theor Math Phys 114 127 (1998)]
  203. Gorsky A, Marshakov A et al Nuclear Physics B 527 690 (1998)
  204. Akhmedov E T Physics Letters B 442 152 (1998)
  205. Zarembo K L, Makeenko Yu M Uspekhi Fizicheskikh Nauk 168 3 (1998)
  206. Aratyn H, Nissimov E, Pacheva S Physics Letters A 244 245 (1998)
  207. Aratyn H, Nissimov E, Pacheva S Physics Letters A 228 164 (1997)
  208. Itoyama H, Morozov A Nuclear Physics B 491 529 (1997)
  209. Vinternits P, Winternitz P i dr Teor. Mat. Fiz. 113 231 (1997)
  210. Orlov A Yu, Winternitz P 38 4644 (1997)
  211. Matone M Journal Of Geometry And Physics 21 381 (1997)
  212. Orlov A Yu, Winternitz P Theor Math Phys 113 1393 (1997)
  213. Yoltukhovskii M V Neurophysiology 29 137 (1997)
  214. Juriev D V Journal Of Geometry And Physics 16 275 (1995)
  215. Semenoff G W, Szabo R J Theor Math Phys 104 823 (1995)
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions