Extended Generalized Uncertainty Principles, Liouville theorem and density of states: Snyder-De Sitter and Yang models
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Abstract
Modifications in quantum mechanical phase space lead to changes in the Heisenberg uncertainty principle, these can result in the Generalized Uncertainty Principle (GUP) or the Extended Uncertainty Principle (EUP), which introduce quantum gravitational effects at small and large distances, respectively. A combination of GUP and EUP, the Extended Generalized Uncertainty Principle (EGUP or GEUP), further generalizes these modifications by incorporating noncommutativity in both coordinates and momenta. This paper examines the impact of EGUP on the Liouville theorem in statistical physics and density of states within non-relativistic quantum mechanics framework. We find a weighted invariant phase space volume element in the cases of Snyder-de Sitter and Yang models, presenting how EGUP alters the density of states, potentially affecting physical (thermodynamical) properties.Keywords
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- Version 1, 2024-09-08, ArXiv
- Version 3, 2025-01-09, ArXiv
- Published version: Nuclear Physics B, 1010.
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