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Title:Weyl Quantization of Fractional Derivatives

Abstract: 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.
 Comments: 9 pages, LaTeX Subjects: Mathematical Physics (math-ph); Quantum Physics (quant-ph) Journal reference: Journal of Mathematical Physics 49 (2008) 102112 DOI: 10.1063/1.3009533 Cite as: arXiv:0907.2699 [math-ph] (or arXiv:0907.2699v1 [math-ph] for this version)

Submission history

From: Vasily E. Tarasov [view email]
[v1] Wed, 15 Jul 2009 20:44:00 UTC (6 KB)
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