Remarks on integration over Lie algebras

Daniel Altschuler; Claude Itzykson

Annales de l'I.H.P. Physique théorique (1991)

  • Volume: 54, Issue: 1, page 1-8
  • ISSN: 0246-0211

How to cite

top

Altschuler, Daniel, and Itzykson, Claude. "Remarks on integration over Lie algebras." Annales de l'I.H.P. Physique théorique 54.1 (1991): 1-8. <http://eudml.org/doc/76519>.

@article{Altschuler1991,
author = {Altschuler, Daniel, Itzykson, Claude},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {matrix models; Wigner statistical model; energy levels; nuclei; integration over Lie algebras; groups},
language = {eng},
number = {1},
pages = {1-8},
publisher = {Gauthier-Villars},
title = {Remarks on integration over Lie algebras},
url = {http://eudml.org/doc/76519},
volume = {54},
year = {1991},
}

TY - JOUR
AU - Altschuler, Daniel
AU - Itzykson, Claude
TI - Remarks on integration over Lie algebras
JO - Annales de l'I.H.P. Physique théorique
PY - 1991
PB - Gauthier-Villars
VL - 54
IS - 1
SP - 1
EP - 8
LA - eng
KW - matrix models; Wigner statistical model; energy levels; nuclei; integration over Lie algebras; groups
UR - http://eudml.org/doc/76519
ER -

References

top
  1. [1] For extensive discussions and references see M.L. Mehta, Random Matrices and the Statistical Theory of Energy Levels, Academic Press, New York, 1967. Zbl0925.60011
  2. [2] G. 't Hooft, Nucl. Phys., Vol. B72, 1974, p. 461; Nucl. Phys., Vol. B75, 1974, p. 461. 
  3. [3] E. Brézin and C. Itzykson, G. Parisi and J.-B. Zuber, Comm. Math. Phys., Vol. 59, 1978, p. 35. Zbl0997.81548MR471676
  4. [4] C. Itzykson and J.-B. Zuber, J. Math. Phys., Vol. 21, 1980, p. 411. Zbl0997.81549MR562985
  5. [5] D. Bessis, C. Itzykson and J.-B. Zuber, Adv. Applied Math., Vol. 1, 1980, p. 109. Zbl0453.05035MR603127
  6. [6] F. David, Nucl. Phys., Vol. B257, 1985, p. 45; V. Kazakov, Phys. Lett., Vol. 150B, 1985, p. 282; V. Kazakov, I. Kostov and A.A. Migdal, Phys. Lett., Vol. B157, 1985, p. 295. 
  7. [7] E. Brézin and V.A. Kazakov, Phys. Lett., Vol. B236, 1990, p. 144; M. Douglas and S. Shenker, Rutgers preprint, 1989; D.J. Gross and A.A. Migdal, Phys. Rev. Lett., Vol. 64, 1990, p. 127. 
  8. [8] V.G. Knizhnik, A.M. Polyakov and A.B. Zamolodchikov, Mod. Phys. Lett., Vol. A3, 1988, p. 819; F. DavidMod. Phys. Lett., Vol. A3, 1988, p. 1651; J. Distler and H. Kawai, Nucl. Phys., Vol. B321, 1989, p. 509. 
  9. [9] J. Harer and D. Zagier, Invent. Math., Vol. 85, 1986, p. 457; R.C. Penner, Bull. A.M.S., Vol. 15, 1986, p. 73; J. Diff. Geom., Vol. 27, 1988, p. 35; Comm. Math. Phys., Vol. 113, 1987, p. 299. Zbl0616.14017MR848681
  10. [10] N. Bourbaki, Groupes et Algèbres de Lie, chapitres 4, 5 et 6, Masson, Paris, 1981. Zbl0483.22001MR647314
  11. [11] D.J. Gross and E. Witten, Phys. Rev., Vol. D21, 1980, p. 446. 
  12. [12] Harish- Chandra, Am. J. Math., Vol. 79, 1957, p. 87. Zbl0072.01901
  13. [13] S. Helgason, Groups and Geometric Analysis, Academic Press, 1984. Zbl0543.58001MR754767
  14. [14] A.A. Kirillov, Funct. Anal. Appl., Vol. 2, 1968, p. 133. Zbl0174.45001
  15. [15] M. Stone, Nucl. Phys., Vol. 314, 1989, p. 557. 
  16. [16] J.J. Duistermaat and G.J. Heckman, Invent. Math., Vol. 69, 1982, p. 259. Zbl0503.58015MR674406
  17. [17] I.B. Frenkel, Invent. Math., Vol. 77, 1984, p. 301. Zbl0548.17007

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.