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

C. Dias, Nuno; N. Prata, João

http://hdl.handle.net/10400.26/57475

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Authors

C. Dias, Nuno

N. Prata, João

Abstract(s)

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

Keywords

noncommutative quantum mechanics non-canonical phase-space deformation of the Heisenberg–Weyl algebra uncertainty principle states of minimal uncertainty variational calculus modulation spaces

URI

http://hdl.handle.net/10400.26/57475

Citation

Dias, 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.