Space and time transformations with a minimal length

Abstract

Phenomenological studies of quantum gravity have proposed a modification of the commutator between position and momentum in quantum mechanics so to introduce a minimal uncertainty in position in quantum mechanics. Such a minimal uncertainty and the consequent minimal measurable length have important consequences on the dynamics of quantum systems. In the present work, we show that such consequences go beyond dynamics, reaching the definition of quantities such as energy, momentum, and the same Hamiltonian. Furthermore, since the Hamiltonian, defined as the generator of time evolution, results to be bounded, a minimal length implies a minimal time.

9 pages, 3 figures

References in corpus (5)

• Universality of Quantum Gravity Corrections
• Quantum Gravity, Dynamical Phase Space and String Theory
• The minimal length is physical
• Comparison of the Semiclassical and Quantum Dynamics of the Bianchi I Cosmology in the Polymer and GUP Extended Paradigms
• Canonical Realizations of Doubly Special Relativity

Cited by in corpus (5)

• 30 years in: Quo vadis generalized uncertainty principle?
• White Paper and Roadmap for Quantum Gravity Phenomenology in the Multi-Messenger Era
• Extended GUP formulation and the role of momentum cut-off
• The minimal length: a cut-off in disguise?
• Momentum gauge fields from curved momentum space through Kaluza-Klein reduction