  The main goal of this work is to study the Dirac oscillator as a quantum
field using the canonical formalism of quantum field theory and to develop the
canonical quantization procedure for this system in $(1+1)$ and $(3+1)$
dimensions. This is possible because the Dirac oscillator is characterized by
the absence of the Klein paradox and by the completeness of its eigenfunctions.
We show that the Dirac oscillator field can be seen as constituted by infinite
degrees of freedom which are identified as decoupled quantum linear harmonic
oscillators. We observe that while for the free Dirac field the energy quanta
of the infinite harmonic oscillators are the relativistic energies of free
particles, for the Dirac oscillator field the quanta are the energies of
relativistic linear harmonic oscillators.
