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Phase operators, phase states and vector phase states for SU(3) and SU(2,1)

Abstract : This paper focuses on phase operators, phase states and vector phase states for the sl(3) Lie algebra. We introduce a one-parameter generalized oscillator algebra A(k,2) which provides a unified scheme for dealing with su(3) (for k < 0), su(2,1) (for k > 0) and h(4) x h(4) (for k = 0) symmetries. Finite- and infinite-dimensional representations of A(k,2) are constructed for k < 0 and k > 0 or = 0, respectively. Phase operators associated with A(k,2) are defined and temporally stable phase states (as well as vector phase states) are constructed as eigenstates of these operators. Finally, we discuss a relation between quantized phase states and a quadratic discrete Fourier transform and show how to use these states for constructing mutually unbiased bases.
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Submitted on : Thursday, April 21, 2011 - 4:16:43 PM
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Mohammed Daoud, Maurice Robert Kibler. Phase operators, phase states and vector phase states for SU(3) and SU(2,1). Journal of Mathematical Physics, American Institute of Physics (AIP), 2011, 52, pp.082101. ⟨10.1063/1.3620414⟩. ⟨in2p3-00587897⟩

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