Abstract
Using the analogy between the spectrum-generating SU(n) approach in particle physics and the dynamical group approach in atomic and molecular physics, we outline the basic ideas behind this alternative to broken-symmetry SU(n) approaches. We review various tests of dynamical SU(3) and SU(4) method, and discuss in particular two crucial tests of the fundamental assumptions.
Research supported in part by NSF grant GF 420(0 and DOE grant E(40-1) 3992.
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References
E.P. Wigner, Ges. Wiss. Gött., Math.-Phys. Klasse (1932) p. 546. Reprinted in “Group Theory and Solid State Physics”, Vol. I, P.H. Meijer, Editor (Gordon and Breach, New York, 1964) pp. 265–278. V. Bargmann, Annals of Math. 59, 1 (1954). G. Ludwig, “Grundlagen der Quantum Mechanik”, (Springer,;954) p. 101.
A.O. Barut and A. Böhm, Phys. Rev. 139B. 1107 (1965).
Y. Dothan, M. Gell-Mann, and Y. Ne'eman, Phys. Rev. Lett. 17. 145 (1965)
N. Mukunda, L. O'Raifeartaigh, and E.C.G. Sudarshan, Phys. Rev. Lett. 15, 1041 (1965).
A. Böhm, “Quantum Mechanics”, Chap. II (Springer, New York, 1978).
This reation was first suggested by J. Werle, in “On a Symmetry Scheme Described by a Non-Lie-Algebra”, ICTP report (Trieste, 1965, unpublished). It was used in A. Böhm, Phys. Rev. 175, 1767 (1968), and in connection with spectrum-generating SU(3) in A. Böhm, Phys. Rev. 158, 1408 (1967); D7, 270 (1973); and A. Böhm and E.C.G. Sudarshan, Phys Rev. 178, 2264 (1969). The present scheme was formulated in A. Böhm and J. Werle, Nucl. Phys. B106, 165 (1976) and in Ref. [7]. The same idea was suggested also by van Dam and Biedenharn (see Ref. [9]).
A. Böhm, Phys. Rev. D13, 2110 (1976).
The theoretical possibility of a mass-dependent correction factor has been noticed several times before: M. Gourdin, in Symmetries and Quark Models, edited by R. Chand (Gordon and Breach, New York, 1970), R.P. Feynman, Photon-Hadron Interaction (Benjamin, New York, 1972), D.R. Yennie, Phys. Rev. Lett. 34, 239 (1975), G.J. Aubrecht II and M.S.K. Razmi, Phys. Rev. D12, 2120 (1975). An octet-brokem SU(3) model incorporating current mixing has been used in L.M. Brown, P. Singer, Phys. Rev. D15, 3438 (1977) where further references are given. Mass dependent correction factors have also been derived from the Duffin-Kemmer-Petiau formalism: B.G. Kenney, D.C. Peaslee and M.M. Nieto, Phys. Rev. D13, 757 (1976), and references therein. The DKP formalism has also other results in common with our dynymical group approach;cf. footnote 16 of Ref. [7]. Another way of describing symmetry breaking effects by mass dependent correction factors in the effective coupling constants has been suggested by J. Schwinger, Proceedings of the 7th Hawaii Topical Conference on Particle Physics, Honolulu (1977) and L.F. Urrutia, “Legtonic and Radiative Meson Decays”, UCLA preprint (1977) (where further references to the description of symmetry breaking effects are given).
H. van Dam and L.C. Biedenharn, Phys. Rev. D14, 405 (1976).
P. Kielanowski, Warsaw University preprint (1978).
D.R. Yennie, Phys. Rev. Lett. 34, 239 (1975)
A. Böhm and R.B. Teese, University of Texas preprint ORO-3992-317 (to appear in Phys. Rev. D).
A. Böhm and R.B. Teese, Phys. Rev. Lett. 38, 629 (1977) and references therein. See also Ref. [121.
R. Settles, in R. Armenteros et al., “Physics from Friends” Geneva, 1978) p. 127.
A. Böhm, Univ. of Texas preprint ORO 316 (to appear in Phys. Rev. D).
K. Kleinknecht, in XVII International Conference on High Energy Physics, J.R. Smith, Editor (London, 1974).
A. Garcia, Phys. Rev. D3. 2638 (1971); D9, 177 (1974; D10, 2839 (1974); and D12, 2692 (1975).
A. Böhm, R.B. Teese, A. Garcia and J.S. Nilsson, Phys. Rev. D15, 689 (1977).
M. Ross, Phys. Lett. 36B, 130 (1971).
A. Böhm, M. Igarashi and J. Werle, Phys. Rev. D15, 2461 (1977).
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Bohm, A., Teese, R.B. (1981). SU(3) and SU(4) as spectrum-generating groups. In: Doebner, HD. (eds) Differential Geometric Methods in Mathematical Physics. Lecture Notes in Physics, vol 139. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10578-6_24
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DOI: https://doi.org/10.1007/3-540-10578-6_24
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