q-analogue of boson commutator and the quantum groups SU sub q (2) and SU sub q (1,1)

Journal Article · Sat Feb 10 00:00:00 EST 1990 · Modern Physics Letters A; (United States)

DOI:https://doi.org/10.1142/S0217732390000287· OSTI ID:5072251

Ui, H; Aizawa, N ^[1]

---

1. Dept. of Physics, Hiroshima Univ., Higashisenda-machi, Naka-ku, Hiroshima 730 (JP)

This paper proposes a defining set of commutation relations to a q-analogue of boson operator; (a{sub q}, a{sup +}{sub q}) = (N + 1){sub q} {minus} (N){sub q}, (N, a{sup +}{sub q}) = a{sup +}{sub q} and (N, a{sub q}) = {minus}a{sub q}, 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 SU{sub q}(1, 1) in addition to that of the SU{sub q}(2) recently proposed by Biedenharn. The explicit form of the number operator is given in terms of a{sub q} and a{sup +}{sub q} and its positive definiteness is proved. A uniqueness of our commutators is also discussed. It is shown that the quantum group SU{sub q}(2) appears as a true symmetry group of a q-analogue of the two-dimensional harmonic oscillator and the SU{sub q}(1, 1) as its dynamical group.

• OSTI ID: 5072251
• Journal Information: Modern Physics Letters A; (United States), Vol. 5:4; ISSN 0217-7323
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOSONS
COMMUTATION RELATIONS
ALGEBRA
DYNAMICAL GROUPS
HARMONIC OSCILLATORS
HEISENBERG PICTURE
QUANTUM FIELD THEORY
SYMMETRY GROUPS
TWO-DIMENSIONAL CALCULATIONS
ELECTRONIC EQUIPMENT
EQUIPMENT
FIELD THEORIES
MATHEMATICS
OSCILLATORS
645400* - High Energy Physics- Field Theory
645300 - High Energy Physics- Particle Invariance Principles & Symmetries