The Sine-Gordon equation has its origins in differential geometry and physical applications in the classical study of coupled oscillatory systems. In the quantum model, it represents a bosonic field with sinusoidal interaction density, which in 1+1 dimensions is equivalent to the massive Thirring model, representing a Dirac field with self-interactions. This equivalence between a bosonic theory and a fermionic theory was first demonstrated through the expansion in perturbative series of both models and the observation that their terms coincide. However, an explicit construction of a solution to the Thirring model can be carried out in terms of the creation and annihilation operators of Sine-Gordon, which allows demonstrating the equivalence between both models, extending the perturbative method and providing insights into the nature of the equivalence between the models.