A fully consistent Lie algebraic representation of quantum phase and number operators

Abstract

A fully consistent realization of the quantum operators corresponding to the canonically conjugate phase and number variables is proposed, resorting to the κ = 1 positive discrete series of the irreducible unitary representation of the Lie algebra su(1, 1) of the double covering group of SO ↑ (1, 2) .T he realization holds in subspace F\|0� , the system Fock space minus the vacuum state. A possible way to extend it to the full space of states based on recourse to a dilated extension of Hilbert space is discussed.