C. Dias, NunoN. Prata, João2025-03-272025-03-272019Dias, N. C., & Prata, J. N. (2019). Uncertainty relations for a non-canonical phase-space noncommutative algebra. Journal of Physics A: Mathematical and Theoretical, 52(22), 225203.http://hdl.handle.net/10400.26/57475We 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 analysisengnoncommutative quantum mechanicsnon-canonical phase-space deformation of the Heisenberg–Weyl algebrauncertainty principlestates of minimal uncertaintyvariational calculusmodulation spacesjournal articlehttps://doi.org/10.1088/1751-8121/ab194b