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We study neutral Dirac particles confined to a family of $(1+2)$-dimensionalwormholes arising from surfaces of revolution with a constant negative Gaussiancurvature, in the framework of a comprehensive effective field theory allowingdeviations from Lorentz symmetry: the gravitational standard-model extension(SME). The Dirac particles are described with a fixed background tensor fieldthat rules the Lorentz symmetry violation in the CPT-even gauge sector of SME.We implement this geometrical approach by incorporating non-minimal couplingsthat possibly induce a Lorentz-symmetry violating term in the modified Diracequation. We also analyze the exact analytical solutions of the correspondingmodified Dirac equation in the presence of a peculiar external magnetic field.

Lorentz violation in a family of $(1+2)$-dimensional wormhole