Number and phase uncertainties of the q-analog quantized field

The q-analog coherent states |z right-angle q are used to identify some of the canonical physical properties of the single-mode q-analog quantized radiation field in the |z right-angle q ''classical limit'' where |z| is large. In this quantum-optics-like limit, the fractional uncertainties of most physical quantities (momentum, position, amplitude, phase) which characterize the quantum field are shown to be O(1), and only vanish as O(1/|z|) when q=1. In contrast to this more-quantum-like behavior for q≠1, the fractional uncertainties do still approach zero for the usual number operator, N, and the N-Hamiltonian HN≡ℎω(N+1/2) which describes a free q-boson gas. An empirical signature for q-boson counting statistics is that (ΔN)2/left-angle N right-angle →0 as |z|→∞. Properties of the q-analog generalizations of the phase operators of Susskind and Glogower (SG) and of the phase operator at signgfq of Pegg and Barnett are investigated. In contrast to the manifest q deformed properties of SG operators for moderate |z|2, the ''Hermitian'' phase operator at signgfq still exhibits almost normal classical behavior in the |z right-angle q basis. In particular, the conventional number-phase uncertainty relation ΔNΔ at signgfq≥1/2 and approximate commutation relation [N,at signgfq]=i are found to follow for the single-mode q-analog quantized field. So N and at signgfq are almost canonically conjugate operators in the |z right-angle q classical limit