NOVEL REPRESENTATION OF ANYONIC STATE GENERATORS

Using the concept of derivative of fractional order, we study the moti on of an electron system in 2 + 1 dimensions under the action of magne tic field. The formalism introduced allows a new insight into the symm etry hidden in the mathematical formulation of quantum mechanics. We s how that the single-electron excitation within the lowest Landau level can be assumed as a composite bi-anyon particle. Moreover, we show an intimate connection between the concept of derivative of noninteger o rder and anyon raising and lowering operators. We show that the formal ism derived by us can be useful in the description of the itinerant el ectrons in the quantum Hall regime.