  After a brief introduction recalling how, in the limit in which the mass and
the electric charge of the electron and the positron tend to zero, Quantum
Electrodynamics reduces to a collection of uncoupled quantum supersymmetric
harmonic oscillators, the phase operator of the quantum fermionic harmonic
oscillator and of the quantum supersymmetric harmonic oscillator are introduced
and their properties analyzed. It is then shown that the phase operator of a
supersymmetric harmonic oscillator is a Goldstone operator at any strictly
positive temperature (finite or infinite).
