Group Theoretical Quantization of Phase and Modulus Related to   Interferences
  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. 
H.A. Kastrup (RWTH Aachen, Germany)