Uncertainty relations for a non-canonical phase-space noncommutative algebra

Abstract

We consider a non-canonical phase-space deformation of the Heisenberg-Weyl algebra that was recently introduced in the context of quantum cosmology. We prove the existence of minimal uncertainties for all pairs of non-commuting variables. We also show that the states which minimize each uncertainty inequality are ground states of certain positive operators. The algebra is shown to be stable and to violate the usual Heisenberg-Pauli-Weyl inequality for position and momentum. The techniques used are potentially interesting in the context of time-frequency analysis.

32 pages

References in corpus (10)

• Heisenberg's Uncertainty Principle
• Weyl-Wigner Formulation of Noncommutative Quantum Mechanics
• Berry Phase in the Gravitational Quantum Well and the Seiberg-Witten map
• Magnetic fields in noncommutative quantum mechanics
• q-deformed noncommutative cat states and their nonclassical properties
• Time-dependent q-deformed coherent states for generalized uncertainty relations
• Non-Canonical Phase-Space Noncommutativity and the Kantowski-Sachs singularity for Black Holes
• Minimal Scales from an Extended Hilbert Space
• Noncommutative Double Scalar Fields in FRW Cosmology as Cosmical Oscillators
• Noncommutative space and the low-energy physics of quasicrystals