Canonical quantization of the Dirac oscillator field in (1+1) and (3+1) dimensions

摘要

he main goal of this work is to study the Dirac oscillator as a quantum field usingthe canonical formalism of quantum field theory and to develop the canonical quantizationprocedure for this system in (1 + 1) and (3 + 1) dimensions. This is possible because the Diracoscillator is characterized by the absence of the Klein paradox and by the completeness of itseigenfunctions. We show that the Dirac oscillator field can be seen as constituted by infinitedegrees of freedom which are identified as decoupled quantum linear harmonic oscillators. Weobserve that while for the free Dirac field the energy quanta of the infinite harmonic oscillatorsare the relativistic energies of free particles, for the Dirac oscillator field the quanta are theenergies of relativistic linear harmonic oscillators.