Phenomenology of the Pauli exclusion principle violations due to the non-perturbative generalized uncertainty principle

New phenomenological implications of the Gen- eralized Uncertainty Principle (GUP), a modification of the HeisenbergUncertaintyPrinciple(HUP) areexploredinlight of constraints arising from underground experiments. An intimate link intertwines the symplectic structure of a the- ory, which is at the very base of the formulation of the HUP and thus a pillar of quantum mechanics, with the sym- metries of space-time and the spin-statistics. Within this wide framework, a large class of non-perturbative GUPs inevitably lead to energy-dependent violations of the total angular momentum conservation rules, and imply hence tiny Pauli Exclusion Principle (PEP) violating transitions. Exotic PEP violating nuclear transitions can be tested, for exam- ple, through extremely high precision data provided by the DAMA/LIBRA experiment. We show that several GUP vio- lations are already ruled out up to the quantum gravity Planck scale.