Fractional charges and fractional spins for composite fermions in quantum electrodynamics

Abstract

By using the Faddeev—Senjanovic path integral quantization method, we quantize the composite fermions in quantum electrodynamics (QED). In the sense of Dirac's conjecture, we deduce all the constraints and give Dirac's gauge transformations (DGT). According to that the effective action is invariant under the DGT, we obtain the Noether theorem at the quantum level, which shows the fractional charges for the composite fermions in QED. This result is better than the one deduced from the equations of motion for the statistical potentials, because this result contains both odd and even fractional numbers. Furthermore, we deduce the Noether theorem from the invariance of the effective action under the rotational transformations in 2-dimensional (x, y) plane. The result shows that the composite fermions have fractional spins and fractional statistics. These anomalous properties are given by the constraints for the statistical gauge potential.