2001/07/31 by Gilad Gour
Physics and Astronomy · #quant-ph #gr-qc #hep-th #physics.optics
published as Found.Phys. 32 (2002) 907-926 · 21 pages, REVTEX
arxiv created 2002/03/11 · arxiv updated 2009/11/30
Defining the observable \bf ϕ canonically conjugate to the number observable \bf N has long been an open problem in quantum theory. The problem stems from the fact that \bf N is bounded from below. In a previous work we have shown how to define the absolute phase observable \bf Φ≡ |\bfϕ| by suitably restricting the Hilbert space of x and p like variables. Here we show that also from the classical point of view, there is no rigorous definition for the phase even though it's absolute value is well defined.