We develop simple computational techniques for constructing all possible SU(3) representations in terms of irreducible SU(3) Schwinger bosons. We show that these irreducible Schwinger oscillators make SU(3) representation theory as simple as SU(2). The new Schwinger oscillators satisfy certain Sp(2,R) constraints and solve the multiplicity problem as well. These SU(3) techniques can be generalized to .
REFERENCES
1.
M.
Moshinsky
, Rev. Mod. Phys.
34
, 813
(1962
);J. J.
De Swart
, Rev. Mod. Phys.
35
, 916
(1963
);M.
Resnikoff
, J. Math. Phys.
8
, 63
(1967
);P.
Jasselette
, Nucl. Phys. B
1
, 521
(1967
);P.
Jasselette
, Nucl. Phys. B
1
, 529
(1967
);M. F.
O’Reilly
, J. Math. Phys.
23
, 2022
(1982
);A. J.
Macfarlane
, L. O.
O’Raifeartaigh
, and P. S.
Rao
, J. Math. Phys.
8
, 536
(1967
);L. C.
Biedenharn
, J. Math. Phys.
4
, 436
(1963
);I. N.
Bemstein
, I. M.
Gelfand
, and S. I.
Gclfand
, Gelfand 1976 Proc Pefrovskij Sem. 2 3
, reprinted in Gelfand I 1988 Collected Works Vol. I1
(Springer
, Berlin
, 1976
), p. 464
;R.
Anishetty
, H.
Gopalkrishna Gadiyar
, M.
Mathur
, and H. S.
Sharatchandra
, Phys. Lett. B
271
, 391
(1991
).2.
J. S.
Prakash
and H. S.
Sharatchandra
, J. Math. Phys.
37
, 6530
(1996
) and references cited therein;J. S.
Prakash
and H. S.
Sharatchandra
, J. Phys. A
26
, 1625
(1993
).3.
M.
Mathur
and D.
Sen
, J. Math. Phys.
42
, 4181
(2001
).4.
S.
Chaturvedi
and N.
Mukunda
, J. Math. Phys.
43
, 5262
(2002
).5.
J.
Schwinger
, U.S. Atomic Energy Commission
Report No. NYO-3071, 1952
;6.
E. R.
Marshalek
, Phys. Rev. C
11
, 1426
(1975
).7.
A.
Auerbach
, Interacting Electrons and Quantum Magnetism
(Springer
, Berlin
, 1994
);N.
Read
and S.
Sachdev
, Nucl. Phys. B
316
, 609
(1989
).8.
M.
Gunaydin
and C.
Saclioglu
, Commun. Math. Phys.
87
, 159
(1982
);9.
M.
Mathur
, Nucl. Phys. B
779
, 32
(2007
);M.
Mathur
, J. Phys. A
38
, 10015
(2005
);10.
F.
Girelli
and E. R.
Livine
, Class. Quantum Grav.
22
, 3295
(2005
);N. D.
Hari Dass
and M.
Mathur
, Class. Quantum Grav.
24
, 2179
(2007
).11.
12.
S.
Coleman
, J. Math. Phys.
5
, 1343
(1964
).13.
14.
R.
Anishetty
, M.
Mathur
, and I.
Raychowdhury
(unpublished).15.
M.
Mathur
and H. S.
Mani
, J. Math. Phys.
43
, 5351
(2002
).© 2009 American Institute of Physics.
2009
American Institute of Physics
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