Explicit quantization of anyon superconductivity Lagrangian

The explicit quantization of the Lagrangian describing anyon super conductivity is performed using the Dirac-Bergmann method. At first, it is pointed out that it is not possible to choose the gauge-fixing condition a(0) = 0 (with the Coulomb gauge). Secondly, the canonical commutation relations between operators are obtained. Thirdly, the correct effective Hamiltonian is derived. Also, the spontaneous projectivation is discussed. Finally, it is shown that by solving the constraints, the Meissner effect is obtained.