  We derive the basic canonical brackets amongst the creation and annihilation
operators for a two (1 + 1)-dimensional (2D) gauge field theoretic model of an
interacting Hodge theory where a U(1) gauge field (A_\mu) is coupled with the
fermionic Dirac fields (\psi and \bar \psi). In this derivation, we exploit the
spin-statistics theorem, normal ordering and the strength of the underlying six
infinitesimal continuous symmetries (and the concept of their generators) that
are present in the theory. We do not use the definition of the canonical
conjugate momenta (corresponding to the basic fields of the theory) anywhere in
our whole discussion. Thus, we conjecture that our present approach provides an
alternative to the canonical method of quantization for a class of gauge field
theories that are physical examples of Hodge theory where the continuous
symmetries (and corresponding generators) provide the physical realizations of
the de Rham cohomological operators of differential geometry at the algebraic
level.
