Fractional Canonical Quantizationof the Free Electromagnetic Lagrangian Density

Abstract

We reformulated the fractional free electromagnetic Lagrangian density using the radiation (Coulomb) gauge and Lorentz gauge. We also obtained fractional EulerLagrange (E-L) equations resulting from these Lagrangian densities. Then we found fractional Hamiltonian density in general form and used Dirac algebraic method to determine the creation and annihilation operators to construct the Canonical Commutation Relations (CCRs).
Keywords: Canonical quantization; Coulomb gauge; Lorentz gauge; Fractional derivative; Free electromagnetic lagrangian density.