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Michel, Louis; Radicati, Luigi A.

The geometry of the octet. (English) Zbl 0267.22019

Ann. Inst. Henri Poincaré, Nouv. Sér., Sect. A 18, 185-214 (1973).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
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Cited in 12 Documents

MSC:

22E70 Applications of Lie groups to the sciences; explicit representations
22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
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References:

[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 .
[3] Evolution of Particle Physics (dedicated to E. Amaldi), Academic Press , New York , 1970 , p. 191 .
[4] Ann. Phys. , t. 66 , 1971 , p. 758 .
[5] 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 .
[6] 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 ).
[7] 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 .
[8] 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 ).
[9] 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 .
[10] 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 · Zbl 0109.40002
[11] 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 · Zbl 0147.42302
[12] 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 · Zbl 0255.57019
[13] Geometrical aspects of symmetry breaking (Proceedings of the 3rd GIFT Seminar in Theoretical Physics, University of Madrid , 1972 p. 49 - 131 .)
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