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 Di...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 tile composite fermions in QBD. 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. Purthermore, 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.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11047020 and 11047173)the Natural Science Foundation of Shandong Province, China (Grant Nos. ZR2011AM019, ZR2010AQ025, BS2010DS006, and Y200814)the Scientific and Technological Development Project of Shandong Province, China (Grant No. J08LI56)
文摘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 tile composite fermions in QBD. 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. Purthermore, 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.
