Abstract
Abstract We construct a pseudo-vector model and realize the rotation transformation for the SU(2) and SU(1,1) dynamics. We introduce concepts of the pseudo-scalar and the scalar product in quantum optics. Several equivalents of the SU(2) and SU(1,1) unified rotation operator are given. By using this method, the two- and three-level Jaynes-Cummings model is discussed in the non-rotating wave approximation.
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