  A typical classical interference pattern of two waves with intensities I_1,
I_2 and relative phase phi = phi_2-phi_1 may be characterized by the 3
observables p = sqrt{I_1 I_2}, p cos\phi and -p sin\phi. They are, e.g. the
starting point for the semi-classical operational approach by Noh, Fougeres and
Mandel (NFM) to the old and notorious phase problem in quantum optics.
Following a recent group theoretical quantization of the symplectic space S =
{(phi in R mod 2pi, p > 0)} in terms of irreducible unitary representations of
the group SO(1,2) the present paper applies those results to that controversial
problem of quantizing moduli and phases of complex numbers: The Poisson
brackets of the classical observables p cos\phi, -p sin\phi and p > 0 form the
Lie algebra of the group SO(1,2). The corresponding self-adjoint generators
K_1, K_2 and K_3 of that group may be obtained from its irreducible unitary
representations. For the positive discrete series the modulus operator K_3 has
the spectrum {k+n, n = 0, 1,2,...; k > 0}. Self-adjoint operators for cos phi
and sin phi can be defined as ((1/K_3)K_1 + K_1/K_3)/2 and -((1/K_3)K_2 +
K_2/K_3)/2 which have the theoretically desired properties for k > or = 0.5.
The approach advocated here solves, e.g. the modulus-phase quantization problem
for the harmonic oscillator and appears to provide a full quantum theoretical
basis for the NFM-formalism.
