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On the fractional minimal length Heisenberg-Weyl uncertainty relation from fractional Riccati generalized momentum operator. (English) Zbl 1198.81181

Summary: It is shown that the minimal length Heisenberg-Weyl uncertainty relation may be obtained if the ordinary momentum differentiation operator is extended to its fractional counterpart, namely the generalized fractional Riccati momentum operator of order \(0 < \beta \leq 1\). Some interesting consequences are exposed. The fractional theory integrates an absolute minimal length and surprisingly a non-commutative position space.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:

81T75 Noncommutative geometry methods in quantum field theory
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