非Abel Chern-Simons理论中量子水平的分数自旋性质

与经典水平下的研究不同，研究了（2＋1）维含非Abel Chern-Simons 项的非线性σ模 型量子水平的分数自旋性质.根据约束Hamilton系统的Faddeev-Senjanovic(FS)路径积分量 子化方案,对该系统进行量子化，由量子Noether定理给出了量子守恒角动量，说明了在量子 水平上该系统仍具有分数自旋的性质. 关键词： 约束Hamilton系统 分数自旋 O(3)非线性σ模型     

Quantum Symmetry of a Chern–Simons System Coupled to a Polaron

The property of fractional spin of the system with Chern–Simons (CS) term coupled to polaron at the quantum level is studied. According to the rule of path integral quantization for constrained Hamiltonian system in Faddeev–Senjanovic (FS) scheme, this system is quantized. Based on the quantal Noether theorem, the quantal conserved angular momentum and the fractional spin at the quantum level of this system is presented. The fractional spin is also presented in the system including Maxwell kinetic term.     

Fractional Spin of System with Chern–Simons Term Coupled to Polaron

The fractional spin of a system with Chern–Simons (CS) term coupled to a polaron at the quantum level is studied. The Faddeev–Senjanovic (FS) scheme for path-integral quantization of constrained Hamiltonian systems is applied. The quantal conserved angular momentum and the fractional spin at the quantum level of this system are presented based on the quantal Noether theorem. The fractional spin is also presented for the system with Maxwell kinetic term.     

含Hopf项和Maxwell-Chern-Simons项O(3)非线性σ模型的分数自旋和分数统计性质

研究了（2＋1）维时空中含Hopf项和Maxwell-Chern-Simons(MCS)项的非线性σ模型的分数自旋性质.根据约束Hamilton系统的Faddeev-Senjanovic(FS)路径积分量子化方案,对该系统进行量子化，由量子Noether定理给出了量子守恒角动量，说明了在量子水平上该系统仍具有分数自旋的性质. 关键词： 约束Hamilton系统 分数自旋 O(3)σ模型     

高阶微商规范不变系统的整体对称性和量子守恒律

分别从Faddeev–Popov(FP)和Faddeev–Senjanovic(FS)路径积分量子化方法对高阶微商规范不变系统导致的位形空间和相空间生成泛函出发,导出规范系统在量子水平下的守恒律,用于高阶Maxwell非AbelChern–Simons(CS)理论.得到了高阶Maxwell非AbelCS理论与标量场耦合系统的量子BRS守恒荷和量子守恒角动量,无论从位形空间或相空间的生成泛函出发,其结果是相同的.并对CS理论中的分数自旋性质给予了讨论.     

The Quantal Canonical Symmetries for a Singular Lagrangian System with Subsidiary Constraints

The quantization for a system containing subsidiary constraints (in configuration space) with a singular Lagrangian is studied, in certain case which can be brought into the theoretical framework of constrained Hamiltonian system. A modified Dirac-Bergmann algorithm for the calculation of all phase-space constraints in those systems is derived. The path integral quantization is formulated by using the Faddeev-Senjanovic scheme. The classical and quantum canonical symmetries (Noether theorem in canonical formalism) are established for such a system. An example is given to illustrate that the connection between the symmetry and conservation law in classical theory are not always validity in the quantum theory.     

Fractional Spin in Non-Abelian Chern-Simons Theories at the Quantum level

Based on the quantization of constrained Hamiltonian system, the quantal conserved laws can be established under the global symmetry transformation. The application of the results to non-Abelian Chern-Simons theory, we can show that property of fractional spin is still preserved at the quantum level in the non-Abelian Chern-Simons theory.     

含Chern-Simons项的旋量电动力学的量子正则对称性

构造了含Chern-Simons(CS)项的旋量电动力学的规范变换生成元.按约束Hamilton系统的Faddeev-Senjanovic(FS)路径积分量子化方案,给出了该系统Green函数的相空间生成泛函;导出了正则Ward恒等式;分析了系统的量子守恒角动量,指出它具有分数自旋性质.     

Quantal Canonical Symmetries in Spinor QED with Chern-Simons Term

The generator of gauge transformation for spinor QED with Chern-Simons (CS) term has been constructed. According to the rule of path integral quantization for constrained system in Faddeev-Senjanovic scheme, the phase-space generating of Green function is obtained, and canonical Ward identities for such a system is also derived. The quantal conserved angular momentum for spinor QED with CS term is studied. The property of fractional spin of the system is pointed out.     

Symmetries in a Constrained System with a Singular Higher-Order Lagrangian

A simple algorithm to construct the generator of gauge transformation for a constrained canonical system with a singular higher-order Lagrangian in field theories is developed. Based on phase-space generating functional of Green function for such a system, the generalized canonical Ward identities under the non-local transformation have been deduced. For the gauge-invariant system, based on configuration-space generating functional, the generalized Ward identities under the non-local transformation have been also derived.The conservation laws are deduced at the quantum level. The applications of the above results to the gauge invariance massive vector field and non-Abelian Chern–Simons(CS) theories with higher-order derivatives are given, a new form of gauge-ghost proper vertices, and Ward–Takahashi identity under BRS transformation and BRS charge at the quantum level are obtained. In the canonical formulation one does not need to carry out the integration over canonical momenta in phase-space path integral as usually performed.     

高阶微商场论中奇异拉氏量系统的量子正则对称性

给出了高阶徽商场论中奇异拉氏量系统规范生成元的构成.从相空间中Green函数的生成泛函出发,导出了约束Hamilton系统正则形式的Ward恒等式.指出该系统的量子正则方程与由Dirac猜想得到的经典正则方程不同.给出了与Chern-Simons理论等价的一个广义动力学系统的量子化.将正则Ward恒等式初步应用于该系统,不作出对正则动量的路径积分,也可导出场的传播子与正规顶角之间的某些关系.     

Quantal global symmetry for a gauge-invariant system

Based on the configuration-space generating functional obtained by using the Faddeev-Popov trick for a gauge-invariant system, the Ward identities for global transformation are derived. The conservation laws at the quantum level for global symmetry transformation are also deduced. A preliminary application of the present formulation to non-Abelian Chern-Simons (CS) theory is given. The Ward identity and quantal BRS charge under the BRS transformation are deduced. The quantal conserved angular momentum is obtained and the fractional spin for CS theories is discussed.     

Exact solutions of a spin-orbit coupling model in two-dimensional central-potentials and quantum-classical correspondence

In this paper we present both the classical and quantum periodic-orbits of a neutral spinning particle constrained in two-dimensional central-potentials with a cylindrically symmetric electric-field in addition, which leads to an effective non-Abelian gauge field generated by the spin-orbit coupling. Coherent superposition of orbital angular-eigenfunctions obtained explicitly under the condition of zero-energy exhibits the quantum-classical correspondence in the meaning of exact coincidence between classical orbits and spatial patterns of quantum wave-functions, which as a consequence results in the fractional quantization of orbital angular-momentum by the requirement of the same rotational symmetry of quantum and classical orbits. A non-Abelian anyon-model emerges in a natural way.     

含Maxwell–Chern–Simons项CP1非线性σ模型的分数自旋和分数统计性质

在(2+1)维时空中研究了含Maxwell-Chern-Simons(MCS)项的CP¹非线性σ模型的量子对称性质.取库仑规范,用Faddeev-Senjanovic路径积分量子化方案对该系统进行量子化.根据约束Hamilton系统的量子对称性质,在量子水平上得到了系统分数自旋性质     

Quantum Symmetries in the Maxwell–Chern–Simons Theory Coupled to Scalar Fields

The Maxwell-Chern-Simons gauge theory coupled to a complex scalar field is quantized in the Becchi-Rouet-Stora-Tyutin (BRST) path integral formalism. On the basis of the symmetries of a constrained canonical (Hamiltonian) system, we get the quantal conserved angular momentum of the system under the global symmetry transformation. It is shown that fractional spin also appears at the quantum level. The canonical Ward identities for this system are derived under local gauge transformation.     

Cliffordization, spin, and fermionic star products

Deformation quantization is a powerful tool for quantizing theories with bosonic and fermionic degrees of freedom. The star products involved generate the mathematical structures which have recently been used in attempts to analyze the algebraic properties of quantum field theory. In the context of quantum mechanics they provide a quantization procedure for systems with either bosonic or fermionic degrees of freedom. We illustrate this procedure for a number of physical examples, including bosonic, fermionic, and supersymmetric oscillators. We show how non-relativistic and relativistic particles with spin can be naturally described in this framework.     

The Transformation Properties at the Quantum Level in Field Theories for a Gauge-Invariant System with a Higher-Order Lagrangian

Based on the configuration-space generating functional of the Green functions for the gauge-invariant system in higher-order derivatives theories, the equations of the transformation properties at the quantum level have been derived. It follows that the sufficient conditions are found which implies that there exists the conservation laws and the expressions of the quantal conserved laws are also given. Applying the results to the non-Abelian Chern-Simons higher-order derivatives theories, the quantal BRST conserved charge and other conserved charges are found, the transformation properties of the conformal transformation at the quantum level is discussed, the quantal conserved angular momentum is derived, it is pointed out that fractional spin in this system may be also preserved in quantum theories. But the connection between the symmetries and conservation laws in classical theories are not always preserved in quantum theories.     

Quantal Noether Identities and Their Applications

Based on the phase-space generating functional of the Green function for a system with a regular/singular Lagrangian, the quantal canonical Noether identities (NI) under the local and non-local transformation in extended phase have been derived, respectively. The result holds true whether the Jacobian of the transformation is equal to unity or not. Based on the configuration-space generating functional of the gauge-invariant system obtained by using Faddeev-Popov (FP) trick, the quantal NI under the local and non-local transformation in configuration space have been also deduced. It is showed that for a system with a singular Lagriangian one must use the effective action in the quantal NI instead of the classical action in corresponding classical NI. It is pointed out that in certain cases, the quantal NI may be converted into the quantal (weak) conservation laws by using the quantal equations of motion. This algorithm to derive the quantal conservation laws differs from the quantal first Noether theorem. The preliminary applications of this formulation to Yang-Mills (YM) fields and non-Abelian Chern-Simons (CS) theories are given. The quantal conserved quantities for non-local transformation in YM fields are obtained. The conserved BRS and PBRS quantities at the quantum level in non-Abelian CS theories are also found. The property of fractional spin in CS theories is discussed. PACS no11.10. Ef; 11.30.−j 11.15. −q.     

The symmetries in the Maxwell－Chern－Simons theory coupled to matter fields

The Maxwell－Chern－Simons gauge theory coupled to a complex scalar field is quantized in the Becchi－Rouet－Stora－Tyutin path integral formalism. Based on the symmetries of a constrained canonical (Hamiltonian) system, we obtain the quantal conserved angular momentum of the system under the global symmetry transformation. It is shown that fractional spin also appears at the quantum level. The canonical Ward identities for this system are derived under local gauge transformation.