Fractional charges and fractional spins for composite fermions in quantum electrodynamics

doi:10.1088/1674-1056/21/7/070501

中国物理B ›› 2012, Vol. 21 ›› Issue (7): 70501-070501.doi: 10.1088/1674-1056/21/7/070501

Fractional charges and fractional spins for composite fermions in quantum electrodynamics

王永龙^{a b c}, 卢伟涛^{a b}, 蒋华^{a b}, 许长谭^a, 潘洪哲^{a b}

a Department of Physics, School of Science, Linyi University, Linyi 276005, China;
b Institute of Condensed Matter Physics, Linyi University, Linyi 276005, China;
c Center for Theoretical Physics, Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

收稿日期:2011-12-31 修回日期:2012-02-20 出版日期:2012-06-01 发布日期:2012-06-01
基金资助:
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), and the Scientific and Technological Development Project of Shandong Province, China (Grant No. J08LI56).

Fractional charges and fractional spins for composite fermions in quantum electrodynamics

Wang Yong-Long(王永龙)^a)b)c)†, Lu Wei-Tao(卢伟涛)^a)b), Jiang Hua(蒋华)^a)b) Xu Chang-Tan(许长谭)^a), and Pan Hong-Zhe(潘洪哲)^a)b)

a Department of Physics, School of Science, Linyi University, Linyi 276005, China;
b Institute of Condensed Matter Physics, Linyi University, Linyi 276005, China;
c Center for Theoretical Physics, Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Received:2011-12-31 Revised:2012-02-20 Online:2012-06-01 Published:2012-06-01
Contact: Wang Yong-Long E-mail:wangyonglong@lyu.edu.cn
Supported by:
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), and the Scientific and Technological Development Project of Shandong Province, China (Grant No. J08LI56).

摘要/Abstract

摘要： 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.

关键词: constrained Hamiltonian systems, Faddeev--Senjanovic path integral quantization formalism, Noether theorem

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.

Key words: constrained Hamiltonian systems, Faddeev--Senjanovic path integral quantization formalism, Noether theorem

中图分类号: (Fractional statistics systems)

05.30.Pr

11.10.Ef (Lagrangian and Hamiltonian approach) 11.15.Yc (Chern-Simons gauge theory)

王永龙, 卢伟涛, 蒋华, 许长谭, 潘洪哲 . Fractional charges and fractional spins for composite fermions in quantum electrodynamics[J]. 中国物理B, 2012, 21(7): 70501-070501.

Wang Yong-Long(王永龙), Lu Wei-Tao(卢伟涛), Jiang Hua(蒋华) Xu Chang-Tan(许长谭), and Pan Hong-Zhe(潘洪哲) . Fractional charges and fractional spins for composite fermions in quantum electrodynamics[J]. Chin. Phys. B, 2012, 21(7): 70501-070501.

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Fractional charges and fractional spins for composite fermions in quantum electrodynamics

Fractional charges and fractional spins for composite fermions in quantum electrodynamics

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