Fractional Quantum Hall Effect and (2 + 1)-Dimensional Quantum Electrodynamics

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Abstract

By investigating the gap equation defining the full electron propagator in the framework of (2 + 1)-dimensional quantum electrodynamics, we derive the fractional quantum Hall effect at the filling factors v = 1/2, 1/3, 2/5, 1/9. In particular, the value v = 1/2 emerges as the lowest order of the development of this gap equation.

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