  Dirac's oscillator (DO) is one of the most studied systems in the
Relativistic Quantum Mechanics and in the physical-mathematics. In particular,
we show that this system has an unique property which it has not ever seen in
other known systems: According to its spatial dimensionality, DO represent
physical systems with very different electromagnetic nature. So far in the
literature, it has been proved using the covariant method the gauge invariance
of the Dirac's oscillator potential. It has also shown that in (3+1)dimensions
the DO represents a relativistic and electrically neutral fermion with magnetic
dipole momentum, into a dielectric medium with spherical symmetry and under the
effect of an electric field which depends of the radial distance. In this
work,and using the same methodology, we show that (2+1) dimensional DO
represents a 1/2-spin relativistic fermion under the effect of a uniform and
perpendicular external magnetic field; whereas in (1+1) dimensions DO
reproduces a relativistic and electrically charged fermion interacting with a
linear electric field. Additionally, we prove that DO does not have chiral
invariance, independent of its dimensionality, due to the interaction potential
which breaks explicitly the chiral symmetry $U(1)_R \times U(1)_L$ but it
preserves the global gauge symmetry $U(1)$.
