Weyl Quantization of Fractional Derivatives

Details Weyl Quantization of Fractional Derivatives Weyl Quantization of Fractional Derivatives

2009-07-15

arxiv.org/abs/0907.2699v1

Journal of Mathematical Physics 49 (2008) 102112

Physics

Mathematical Physics

9 pages, LaTeX

Scientific paper

The quantum analogs of the derivatives with respect to coordinates q_k and momenta p_k are commutators with operators P_k and $Q_k. We consider quantum analogs of fractional Riemann-Liouville and Liouville derivatives. To obtain the quantum analogs of fractional Riemann-Liouville derivatives, which are defined on a finite interval of the real axis, we use a representation of these derivatives for analytic functions. To define a quantum analog of the fractional Liouville derivative, which is defined on the real axis, we can use the representation of the Weyl quantization by the Fourier transformation.

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