This work explores a Standard Model (S.M.) extension possibility, that violates Lorentz invariance, preserving the space-time isotropy and homogeneity. In this sense HMSR represents an attempt to introduce an isotropic Lorentz Invariance Violation in the elementary particle S.M. The theory is constructed starting from a modified kinematics, that takes into account supposed quantum effects due to interaction with the space-time background. The space-time structure itself is modified, resulting in a pseudo-Finsler manifold. The S.M. extension here provided is inspired by the effective fields theories, but it preserves covariance, with respect to newly introduced modified Lorentz transformations. Geometry perturbations are not considered as universal, but particle species dependent. Non universal character of the amended Lorentz transformations allows to obtain visible physical effects, detectable in experiments by comparing different perturbations related to different interacting particles species.
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