Fractional Spin And Fractional Statistics Properties Of The Chern-simons Theory Study

There is an interest in searching for dynamical system with Chern-Simons term, especially, (2+1) dimensional gauge theories with Chern-Simons (CS) terms lead to the occurrence of fractional spin and statistics. It shows important significance while explaining the quantum Halleffect and high-T_c superconductivity. In this paper we first introduce the constrained Hamiltonsystems briefly, and give several kinds of the quantization scheme, we examine in detail the rule of Faddeev-Senjanovic path integral quantization. Second, the symmetries of the constrained Hamilton system are further introduced, Noether theorem are presented. We discuss the classical and quatum canonical symmetries for a system with higher-order derivatives, Neother theorem and the quantal conserved charge are obtained. Finally, we study the property of factional spin and fractional statistics for the constrained Hamilton system with CS term. Following the fundamental theories of constrained system, the property of fractional spin of Jackiw-Johnson model with CS term in (2+1) dimensions at the quantum level is studied. And we study in detail the property of fractional spin and fractional statistics of O(3) non-linearσmodel withMaxwell-Chern-Simons (MCS) terms in higher-order derivative systems in (2+1) dimensions. The system is quantized in the Faddeev-Senjanovic (FS) path integral formalism. Based on the quantal Noether theorem, the quantal conserved angular momentum is obtained and the fractional spin at the quantum level of this system is presented, and the effect of higher-order derivative terms on angular momentum is discussed.