Generalized Weyl quantization formalism for the cylindrical phase space S 1 × R 1 is developed. It is shown that the quantum observables relevant to the phase of linear harmonic oscillator or electromagnetic field can be represented within this formalism by the self-adjoint operators on the Hilbert space L 2 (S 1 ).
a b s t r a c tA generalized Weyl quantization formalism for a particle on the circle is shown to supply an effective method for defining the number-phase Wigner function in quantum optics. A Wigner function for the stateρ and the kernel K for a particle on the circle is defined and its properties are analysed. Then it is shown how this Wigner function can be easily modified to give the number-phase Wigner function in quantum optics. Some examples of such number-phase Wigner functions are considered.
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