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We deduce the canonical brackets for a two (1 + 1)-dimensional (2D) freeAbelian 1-form gauge theory by exploiting the beauty and strength of thecontinuous symmetries of a Becchi-Rouet-Stora-Tyutin (BRST) invariantLagrangian density that respects, in totality, six continuous symmetries. Thesesymmetries entail upon this model to become a field theoretic example of Hodgetheory. Taken together, these symmetries enforce the existence of exactly thesame canonical brackets amongst the creation and annihilation operators thatare found to exist within the standard canonical quantization scheme. Thesecreation and annihilation operators appear in the normal mode expansion of thebasic fields of this theory. In other words, we provide an alternative to thecanonical method of quantization for our present model of Hodge theory wherethe continuous internal symmetries play a decisive role. We conjecture that ourmethod of quantization is valid for a class of field theories that aretractable physical examples for the Hodge theory. This statement is true in anyarbitrary dimension of spacetime.

Basic Brackets of a 2D Model for the Hodge Theory without its Canonical Conjugate Momenta