Abstract
New phenomenological implications of the Generalized Uncertainty Principle (GUP), a modification of the Heisenberg Uncertainty Principle (HUP) are explored in light of constraints arising from underground experiments. An intimate link intertwines the symplectic structure of a theory, which is at the very base of the formulation of the HUP and thus a pillar of quantum mechanics, with the symmetries 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 example, through extremely high precision data provided by the DAMA/LIBRA experiment. We show that several GUP violations are already ruled out up to the quantum gravity Planck scale.
Highlights
The Heisenberg uncertainty principle immediately implies that identical particles cannot be distinguished anymore in scattering amplitudes
Identical particles with integer spin, namely bosons, undergo scattering amplitudes with construca e-mail: h.shababi@scu.edu.cn tive interference. This is certainly suggesting us how intimately the spin statistics is related to the Heisenberg Uncertainty Principle (HUP)
A natural question would be: what would happen if we modify the very foundations of quantum mechanics, deforming the standard HUP so to account for new physics? May this turn into a modification of the Spin Statistics and the Pauli Exclusion Principle (PEP)?
Summary
The Heisenberg uncertainty principle immediately implies that identical particles cannot be distinguished anymore in scattering amplitudes. Stepping out of the canonicity of theory amounts to change one of the fundamental pillars of quantum mechanics, namely the HUP It was shown in [10] that the relationship between symplectic structure and symmetry structure extends to the co-algebraic structure of the field theories’ symmetries: in other words, the link with between the HUP and the space-time symmetries extends to the statistics. This realization opened the pathway to the formulation in the symplectic geometry approach of the Hopf algebras symmetries, which are associated to non-commutative spacetimes/effective backgrounds instantiations of several quantum gravity models. In forthcoming investigations, we will be back to this topic with the aim to further clarify the link between deformation of the HUP, deformation of the algebra and deformation of the statistics [25]
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