Boson operator realizations of su(2) and su(1,1) and unitarization

1989 ◽  
Vol 30 (3) ◽  
pp. 594-600 ◽  
Author(s):  
H. D. Doebner ◽  
Bruno Gruber ◽  
Miguel Lorente
Keyword(s):  
Boson Operator

q-ANALOGUE OF BOSON COMMUTATOR AND THE QUANTUM GROUPS SUq(2) AND SUq(1, 1)

1990 ◽  
Vol 05 (04) ◽  
pp. 237-242 ◽  
Author(s):  
HARUO UI ◽  
N. AIZAWA
Keyword(s):  
Harmonic Oscillator ◽  
Quantum Group ◽  
Symmetry Group ◽  
Quantum Groups ◽  
Heisenberg Algebra ◽  
Positive Definiteness ◽  
Two Dimensional ◽  
Number Operator ◽  
Boson Operator ◽  
Dynamical Group

We propose a defining set of commutation relations to a q-analogue of boson operator; [Formula: see text], [Formula: see text] and [N, aq]=−aq, which contracts to the Heisenberg algebra of boson operators in the limit of q=1. Here, N is the number operator, [N]q being its q-analogue operator. By making use of this set, we construct a new realization of the “noncompact” quantum group SUq(1, 1) in addition to that of the SUq(2) recently proposed by Biedenharn. The explicit form of the number operator is given in terms of aq and [Formula: see text] and its positive definiteness is proved. A uniqueness of our commutators is also discussed. It is shown that the quantum group SUq(2) appears as a true symmetry group of a q-analogue of the two-dimensional harmonic oscillator and the SUq(1, 1) as its dynamical group.

Generalized measurement of the non-normal two-boson operator

2007 ◽  
Vol 40 (26) ◽  
pp. F531-F537 ◽  
Author(s):  
Matteo G A Paris ◽  
Giulio Landolfi ◽  
Giulio Soliani
Keyword(s):  
Boson Operator ◽  
Generalized Measurement

scholarly journals The su(1,1)-Algebraic Boson Model in the Deformed Boson Scheme: The Second Holstein-Primakoff Representation as q-Deformed Boson Operator

2003 ◽  
Vol 109 (1) ◽  
pp. 77-86
Author(s):  
A. Kuriyama ◽  
C. Providencia ◽  
J. d. Providencia ◽  
Y. Tsue ◽  
M. Yamamura
Keyword(s):  
Boson Operator ◽  
Boson Model

Normal and antinormal ordering of boson operator functions

1985 ◽  
Vol 108 (7) ◽  
pp. 322-324 ◽  
Author(s):  
B.L. Willis ◽  
P.F. Zweifel
Keyword(s):  
Boson Operator ◽  
Operator Functions
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