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The geometry of the octet

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Abstract

The geometry of the octet ANNALES DE L’I. H. P., SECTION A LOUIS MICHEL LUIGI A. RADICATI The geometry of the octet Annales de l’I. H. P., section A, tome 18, no 3 (1973), p. 185-214. <http://www.numdam.org/item?id=AIHPA_1973__18_3_185_0> © Gauthier-Villars, 1973, tous droits réservés. L’accès aux archives de la revue « Annales de l’I. H. P., section A », implique l’accord avec les conditions générales d’utilisation (http://www. numdam.org/legal.php). Toute utilisation commerciale ou impression systé- matique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ 185 The geometry of the octet Louis MICHEL Luigi A. RADICATI Institut des Hautes Etudes Scientifiques 91440 Bures-sur-Yvette, France Scuola Normale Superiore, Pisa, Italy. Ann. Inst. Henri Poincaré, Vol. XVIII, no 3, 1973, Section A : Physique théorique. 1. - INTRODUCTION The adjoint representation of SU (3) plays a specially important role in the physical applications since the electromagnetic and weak currents whose space integrals are the generators of the symmetry belongs to it. In the physical litterature this representation is usually discussed by using a particular basis namely the Gell-Mann [1 ] ~-matrices. To evaluate most of the physical quantities which are functions of the matrix elements of the currents on vectors of the adjoint representation, one has to compute expressions involving products of the tensors components and B/3 These are sines and cosines of angles multiples of 30°. We think there might be advantages in going beyond this trigonome- trical approach by studying the geometry of the 8-dimensional space R8 of the SU (3) adjoint representation. In our opinion this allows to obtain a deeper understanding of the structure of R8, a structure much richer than the one of R on which acts t

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