Abstract
In this paper I consider the general mathematical problem of the polar decomposition of an operator in a linear space. Extending the space makes it possible to define a unitary operator related to the original nonhermitean one. By Stone's theorem this guarantees the existence of a phase operator in the extended space. The connection with supersymmetry is pointed out. Applying the general results to harmonic oscillator creation and annihilation operators we regain a phase description originally introduced by Newton. Projecting the phase operator from the extended space to the original one, we find a phase representation for the Boson operators. Introducing the conjugate rotation operator, one can describe the oscillator dynamics in the phase representation. The connection with the Barnett–Pegg phase operator is pointed out.
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