  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 proposes an application of those results to
the old problem of quantizing modulus and phase in interference phenomena: The
self-adjoint Lie algebra generators K_1, K_2 and K_3 of that group correspond
to the classical observables p cos(phi), -p sin(phi) and p > 0 the Poisson
brackets of which obey that Lie algebra, too. For the irreducible unitary
representations of the positive series the modulus operator K_3 has the
positive discrete spectrum {n+k, n=0,1,2,...; k > 0}. Self-adjoint operators
for cos(phi) and sin(phi) can then be defined as (K_3^{-1}K_1 + K_1 K_3^{-1})/2
and - (K_3^{-1} K_2 + K_2 K_3^{-1})/2 which have the theoretically desired
properties for k >0.32. Some matrix elements with respect to number eigenstates
and with respect to coherent states are calculated. One conclusion is that
group theoretical quantization may be tested by quantum optical experiments.
