A general definition is given of vector‐coherent state (VCS) representation theory. It is shown that the theory is more general than suggested by previous applications and that it incorporates the standard theories of induced representations as special cases. The associated K‐matrix theory is also given a fuller treatment than hitherto and shown to provide a rather general algorithm both for projecting VCS representations from larger representations in which they are embedded and for determining the Hermitian form, with respect to which an isometric‐equivalent representation is, in fact, isometric.
REFERENCES
1.
2.
J. R. Klauder and B-S. Skagerstam, Coherent States; Applications in Physics and Mathematical Physics (World Scientific, Singapore, 1985);
W-M Zhang, D. H. Feng, and R. Gilmore, “Coherent states: Theory and some applications,” preprint, Drexel Univ., 1989.
3.
4.
Generalized Coherent States and their Applications (Springer-Verlag, Berlin, 1985).
5.
6.
D. J.
Rowe
, A.
Ryman
, and G.
Rosensteel
, Phys. Rev. A
22
, 2362
(1980
);P. Kramer and M. Saraceno, “Geometry of the Time-Dependent Variational Principle in Quantum Mechanics,” Lecture Notes in Physics, Vol. 135 (Springer-Verlag, New York, 1982).
7.
B. Kostant, Lecture Notes in Mathematics, Vol. 170 (Springer-Verlag, Berlin, 1970);
J-M. Souriau, Structure des Systemes Dynamigues (Dunod, Paris, 1970).
8.
D. J.
Rowe
, G.
Rosensteel
, and R.
Carr
, J. Phys. A: Math. Gen.
17
, L399
(1984
);D. J.
Rowe
, B. G.
Wybourne
, and P. H.
Butler
, J. Phys. A: Math. Gen.
18
, 939
(1984
);D. J.
Rowe
, G.
Rosensteel
, and R.
Gilmore
, J. Math. Phys.
26
, 2787
(1985
).9.
10.
K. T.
Hecht
, R.
Le Blanc
, and D. J.
Rowe
, J. Phys. A: Math. Gen.
20
, 2241
(1987
).11.
D. J.
Rowe
, R.
Le Blanc
, and K. T.
Hecht
, J. Math. Phys.
29
, 287
(1988
).12.
13.
14.
15.
R.
Le Blanc
and K. T.
Hecht
, J. Phys. A: Math. Gen.
20
, 4613
(1987
);R.
Le Blanc
and L. C.
Biedenharn
, J. Phys. A: Math. Gen.
22
, 31
(1989
);K. T.
Hecht
and L. C.
Biedenharn
, preprint; C.
Quesne
, J. Phys. A: Math. Gen.
24
, 2697
(1991
).16.
D. J. Rowe, “Coherent states, contractions and classical limits of the non-compact symplectic groups,” in Proceeding of the XIIVth International Colloquium on Group Theoretical Methods in Physics, edited by W. W. Zachary (World Scientific, Singapore, 1984);
“Some recent advances in coherent state theory and its applications to nuclear collective motion,” in Phase Space Approach to Nuclear Dynamics, edited by M. de Toro et al., (World Scientific, Singapore, 1985);
O.
Castanos
, E.
Chacon
, M.
Moshinsky
, and C.
Quesne
, J. Math. Phys.
26
, 2107
(1985
);O.
Castãnos
, P.
Kramer
, and M.
Moshinsky
, J. Math. Phys.
27
, 924
(1986
);K. T.
Hecht
, “The vector coherent state method and its application to problems of higher symmetry
,” Lecture Notes in Physics, Vol. 30
, 1415
(1989
); , J. Math. Phys.
K. T.
Hecht
, R.
Le Blanc
, and D. J.
Rowe
, J. Phys. A: Math. Gen.
20
, 257
(1987
);K. T.
Hecht
, R.
Le Blanc
, and D. J.
Rowe
, J. Phys. A: Math. Gen.
20
, 2241
(1987
);R.
Le Blanc
and K. T.
Hecht
, J. Phys. A: Math. Gen.
20
, 4613
(1987
);L. C.
Papaloucas
, J.
Rembielinski
, and W.
Tybor
, J. Math. Phys.
30
, 2406
(1989
);J-Q. Chen, K. T. Hecht, and D. H. Feng, “Vector coherent theory in new perspective—A hybrid mapping from fermion to fermion-boson space,” Drexel Univ. Rep. DUPHY-005, 1990.
17.
Induced Representations of Groups and Quantum Mechanics (Benjamin, New York, 1969).
18.
19.
V. S. Varadarajan, Lie Groups, Lie Algebras and their Representations (Springer-Verlag, New York, 1984) 2nded.;
A. W. Knapp, Representation Theory of Semi-simple Groups (Princeton U.P., Princeton, New Jersey, 1986).
20.
21.
R. Godement, Seminaire Cartan (Ecole Normale Supérieure, Paris, 1958);
22.
23.
G. Giavarini and E. Onofri, “Vector coherent states and non-abelian gauge structures in quantum mechanics,” preprint, 1989.
24.
25.
26.
27.
D. J.
Rowe
, R.
Le Blanc
, and J.
Repka
, J. Phys. A: Math. Gen.
22
, L309
(1989
).28.
D. J.
Rowe
, M. G.
Vassanji
, and J.
Carvalho
, Nucl. Phys. A
504
, 76
(1989
);M. Jarrio, J. L. Wood, and D. J. Rowe, Nucl, Phys. (in press).
29.
30.
L.
Weaver
, L. C.
Biedenharn
, and R. Y.
Cusson
, Ann. Phys. (NY)
77
, 250
(1973
).31.
D. J. Rowe, Nuclear collective motion (Methuen, London, 1970);
A. Bohr and B. R. Mottelson, Nuclear Structure (Benjamin, New York, 1975) Vol. II; P. Ring and P. Schuck, The Nuclear Many-body Problem (Springer-Verlag, Berlin, 1980).
32.
33.
B.
Buck
, L. C.
Biedenharn
, and R. Y.
Cusson
, Nucl. Phys. A
317
, 205
(1979
).34.
35.
A. Klein and E. R. Marshalek, “Boson realizations of Lie algebras with application to nuclear physics,” Univ. of Pennsylvania Rep. No. 0065NT, 1989.
36.
D. J.
Rowe
, P.
Rochford
, and R.
Le Blanc
, Nucl. Phys. A
464
, 39
(1987
).
This content is only available via PDF.
© 1991 American Institute of Physics.
1991
American Institute of Physics
You do not currently have access to this content.