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.

9 pages, LaTeX

References in corpus (3)

• Quantization of non-Hamiltonian and Dissipative Systems
• Fractional Heisenberg Equation
• Map of Discrete System into Continuous

Cited by in corpus (4)

• Review of Some Promising Fractional Physical Models
• Fractional Derivative Regularization in QFT
• Infrared spectroscopy of diatomic molecules - a fractional calculus approach
• Dissipative systems fractionally coupled to a bath