The geometry of the octet
Annales de l'I.H.P. Physique théorique, Tome 18 (1973) no. 3, p. 185-214
@article{AIHPA_1973__18_3_185_0,
author = {Michel, Louis and Radicati, Luigi A.},
title = {The geometry of the octet},
journal = {Annales de l'I.H.P. Physique th\'eorique},
publisher = {Gauthier-Villars},
volume = {18},
number = {3},
year = {1973},
pages = {185-214},
zbl = {0267.22019},
mrnumber = {325036},
language = {en},
url = {http://www.numdam.org/item/AIHPA_1973__18_3_185_0}
}

Michel, Louis; Radicati, Luigi A. The geometry of the octet. Annales de l'I.H.P. Physique théorique, Tome 18 (1973) no. 3, pp. 185-214. http://www.numdam.org/item/AIHPA_1973__18_3_185_0/

[1] M. Gell-Mann, Phys. Rev., t. 125, 1962, p. 1097. | MR 138414

[2] L. Michel and L. Radicati :

(a) Symmetry Principles at High Energy (Fifth Coral Gables Conférence, Benjamin, New-York, 1968, p. 19.)

(b) Atti. Accad. Sci. Torino, Cl. Sci. Fis. Mat. Natur., 1971, p. 377.

(c) Evolution of Particle Physics (dedicated to E. Amaldi), Academic Press, New York, 1970, p. 191.

(d) Ann. Phys., t. 66, 1971, p. 758.

[3] The d-coefficients were introduced for SU (3), by M. Gell-Mann (réf. [1]) and Independently and for all SU (n), by L.C. Biedenharm, J. Math. Phys., vol. 4, 1963, p. 436.

[4] V.I. Ogievetskii and I.V. Polubarinov, This is the oldest paper listing essentially all relations between the f-and d-coefficients for SU (3) (Sov. J. Nucl. Phys., t. 4, 1967, p. 605).

L.M. Kaplan and M. Resnikoff, This paper gives a fairly complete set of relations for all SU (n) (J. of Math. Phys., t. 8, 1967, p. 2194.) After this paper several authors have discussed this type of relations : amongst the others we quote A. Pais, S.P. Rosen, A.J. Macfarlane, A. Subery and P.H. Weisz.

[5] C. Dublemond, This is to our knowledge the only paper where some relation are written in vector form (Ann. of Phys., t. 33, 1965, p. 214).

[6] A study of the invariants and their values for all representations is contained in A.M. Perelemov and V.S. Popov, Sov. J. Nucl. Phys., t. 3, 1966, p. 676, and in J.D. Louck and L.C. Biedenharn, J. Math. Phys., vol. 11, 1970, p. 2368.

[7] The concept of stratum used here is a simple example of that (« strate » in French) defined by R. Thom (L'Enseignement Mathématique, t. 8, 1962, p. 24). | Zbl 0109.40002

[8] This result is due to D. Montgomery and C.T. Yang, For a review paper on the action of compact groups [see D. Montgomery, Differential Analysis (Bombay Colloqum, 1964, p. 43)]. See also L. Michel. | Zbl 0147.42302

(a) Non linear group actions, smooth action of compact Lie-groups on manifolds (Statistical Mechanics and Field Theory, Israel University Press, Jerusalem, 1972, p. 133-150.) | Zbl 0255.57019

(b) Geometrical aspects of symmetry breaking (Proceedings of the 3rd GIFT Seminar in Theoretical Physics, University of Madrid, 1972 p. 49-131.)