Oscillator Representations of the Lie Algebra su(1, 1) and the Quantum Algebra suq(1, 1)

Abstract

It is discussed how the representations of the Lie algebra su(1, 1) and its q-deformation suq(1, 1) are constructed in terms of operators, a, a† and N satisfying [N, a] = -a, [N, a†] = a† and N† = N. It is found that any irreducible unitary representation of su(1, 1) and suq(1, 1) can be described by a, a† and N in an infinite number of ways.