高介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Abel Chern-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，无论从闰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。     

规范理论中的量子守恒荷

从Faddeev-Popov(F-P)方法对规范理论导致的位形空间生成泛函出发,导出了规范系统在量子情形下的守恒律,用于非Abel Chern-Simons(CS)理论,得到了CS场与Fermi场耦合系统的量子BRS守恒荷和量子守恒角动量. 对CS理论中的分数目旋性质给予了讨论.     

非定域量子Noether恒等式及应用

基于高阶微商奇异拉氏量系统的相空间生成泛函,导出了定域和非定域变换下的量子正则Noether恒等式;对高阶微商规范不变系统,导出了位形空间中定域和非定域变换下的量子Noether恒等式.指出在某些情形下,由量子Noether恒等式可导致系统的量子守恒律.这种求守恒律的程式与量子Noether(第一)定理不同.用于高阶微商非AbelChern-Simons(CS)理论,求出某些非定域等变换下的量子守恒量.     

量子水平的Noether恒等式

基于Green函数的相空间生成泛函,导出了定域变换下的量子正则Noether恒等式;对规范不变系统,导出了位形空间中的量子Noether恒等式.指出在某些情形下由量子Noether恒等式可导致系统的量子守恒律,这种求量子守恒律的方法与量子Noether(第一)定理的程式不同.用于非Abel Chern-Simons(CS)理论,求出了BRS和PBRS守恒荷,这两个守恒荷完全不同.     

非定域变换的广义Ward恒等式

基于高阶微商奇异拉氏量系统相空间Green函数的生成泛函,导出了该系统在定域和非定域变换下的广义正则Ward恒等式.对规范不变系统,从位形空间生成泛函出发,导出了该系统在定域、非定域和整体变换下的广义Ward恒等式.用于高阶微商非Abel(Chern-Simons CS)理论,无需作出生成泛函中对正则动量的路径积分,即可导出正规顶角的某些关系.此外还给出了BRS变换下的Ward-Takahashi恒等式.     

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.     

奇异拉氏量系统相空间路径积分中的整体对称性

基于奇异拉氏量系统Green函数的相空间生成泛函,导出了相空间中整体变换下的Ward恒等式和整体对称下的量子守恒律.一般它有别于经典Noether守恒律.用于杨-Mills理论,导出了BRS变换下的Ward-Takahashi恒等式和BRS守恒律;用于非Abel-Chern-Simons理论,导出了系统的量子角动量,它有别于经典角动量在于计及了鬼粒子对角动量的贡献.     

规范不变系统量子水平的变换性质及应用

按Faddeev-Popov路径积分量子化方法,给出规范不变系统在位形空间中的生成泛函,导出了系统位形空间中量子水平的变换性质.讨论了该系统量子水平的守恒律问题,且给出了Poincar群变换下电磁场在介质分界面附近量子水平的变换性质,在量子水平上说明了电磁波反射和折射时能量中心的“横移”现象. 关键词： 规范理论 位形空间 路径积分 “横移”效应     

动力系统的正则量子对称性质

分别从正规和奇异拉氏量系统的相空间生成泛函出发,导出了增广相空间中整体对称下的正则形式Ward恒等式.考虑对应的定域交换,得到了量子水平的守恒荷,给出了正则形式的量子Noether定理.讨论了在核子和π介子相互作用中的初步应用.     

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.     

Canonical Symmetries in the Functional Formalism

Based on the phase-space generating functionalof the Green function, the canonical Ward identities(CWI) under local, nonlocal, and global transformationsin phase space for a system with a regular and singular Lagrangian have been derived. Therelation of global canonical symmetries to conservationlaws at the quantum level is presented. The advantage ofthis formulation is that one does not need to carry out the integration over canonicalmomenta in a phase-space path (functional) integral asin the traditional treatment in configuration space. Ingeneral, the connection between global canonicalsymmetries and conservation laws in classical theories isno longer preserved in quantum theories. Applications ofour formulation to the non-Abelian Chern-Simons (CS)theory are given, and new forms for CS gauge-ghost field proper vertices and the quantal conservedangular momentum of this system are obtained; thisangular momentum differs from the classical one in thatone needs to take into account the contribution of angular momenta of ghost fields.     

Topological Chern—Simons vortices in the O (3) σ -model

Based on the phase-space path integral (functional integral) for a system with a regular or singular Lagrangian, the generalized Ward identities for phase space generating functional under the global transformation in phase space are derived respectively. The canonical Noether theorem at the quantum level is also established. It is pointed out that the connection between the symmetries and conservation laws in classical theories, in general,is no longer preserved in quantum theories. The advantage of our formulation is that we do not need to carry out the integration over the canonical momenta as usually performed. Applying the present formulation to Yang-Mills theory, the quantal BRS conserved quantity and Ward-Takahashi identity for BRS tranformation are derived; the Ward identities for gaugeghost proper vertices and new quantal conserved quantity are also found. In comparison of quantal conservation laws with those one deriving from configuration-space path integral using the Faddeev-Popov(F-P) trick is discussed. A precise study of path-integral quantisation for a nonlinear sigma model with Hopf and Chern-Simons (CS) terms is reexamined. It has been shown that the angular momentum at the quantum level is equal to classical (Noether ) one. Applying our formulation to non-Abelian CS theory, the quantal conserved angular momentum of this system is obtained which differs from classical one in that one needs to take into account the contribution of angular momenta of ghost fields.     

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.     

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.     

Quantal Conserved Charges in Gauge Theory

Starting from the configuration-space generating functional for gauge theory obtained by using the Faddeev-Popov method,the conservation laws at the quantum level for the gauge-invariant system are derived.Appling to non-Abel Chern-Simons(CS)theory,the quantum BRS conserved charge and quantuml conserved angular momentum for the non-Abelian CS fields coupled to Fermion field are deduced.The property of fractional spin in CS theory is discussed.     

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.     

Canonical global symmetry and quantal conservation laws for a system with singular higher order Lagrangian

Starting from the phase-space generating functional of the Green function for a system with singular higher order Lagrangian, the generalized canonical Ward identities under the global symmetry transformation in phase space is deduced. The local transformation connected with this global symmetry transformation is studied, and the quantal conservation laws are obtained for such a system. We give a preliminary application to higher derivative Yang-Mills theory; a generalized quantal BRS conserved quantity is found.