2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/200187The purpose of this work is two fold. Working in the framework of $(1+1)D$ Lorentz violating field theories we will investigate in the first place the general claim that fermionic interactions may be equivalent to a deformation of the canonical structure of the theory. Second the deformed theory will be studied using duality reasoning to address the behavior of the Infra-Red and Ultra-Violet regimes.revtex4 file, 19 pages, typos corrected, reference added, appendix added, accepted for publication in Physical Review DHigh Energy Physics - Theorytext