Non-hermitian observables in non commutative quantum mechanics

Frederik Scholtz

Stellenbosch University, National Institute for Theoretical Physics, Department of Physics, Stellenbosch, South Africa

We argue that position measurements in non commutative quantum mechanics must be weak measurements defined by a positive operator valued measure contructed from the eigenstates of non hermitian operators and that the 'Bopp-shifted' commuting operators cannot be interpreted as representing position. The relation of these cosntructions to the Moyal-Groenewald and Voros planes is also discussed.

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