  We exploit the ideas of spin-statistics theorem, normal-ordering and the key
concepts behind the symmetry principles to derive the canonical
(anti)commutators for the case of a one (0 + 1)-dimensional (1D) N = 2
supersymmetric (SUSY) harmonic oscillator (HO) without taking the help of the
mathematical definition of canonical conjugate momenta with respect to the
bosonic and fermionic variables of this toy model for the Hodge theory (where
the continuous and discrete symmetries of the theory provide the physical
realizations of the de Rham cohomological operators of differential geometry).
In our present endeavor, it is the full set of continuous symmetries and their
corresponding generators that lead to the derivation of basic (anti)commutators
amongst the creation and annihilation operators that appear in the normal mode
expansions of the dynamical fermionic and bosonic variables of our present N =
2 SUSY theory of a HO. These basic brackets are in complete agreement with such
kind of brackets that are derived from the standard canonical method of
quantization scheme.
