Osp(1,2)自旋链的潜藏定域规范不变性

在量子反散射框架内研究了Osp（1，2）自旋链的潜藏定域规范不变性．结果表明，该模型允许AbelU（1）规范变换，其能谱在规范变换下保持不变，而本征矢及Bethe ansatz方程明显与规范变换相关． 关键词：     

相对论自旋流体力学

近年来,随着重离子碰撞实验中超子自旋极化与矢量介子自旋排列现象的发现,关于夸克胶子物质中自旋输运的理论研究也得到蓬勃发展,其中包括相对论自旋流体力学,它是描述自旋输运的流体力学理论.本文对相对论自旋流体力学的近期发展进行了综述,主要包括以下内容:1)相对论自旋流体力学基本方程的推导,包括宏观的唯象学推导、基于有效场论的推导以及基于输运理论的推导; 2)该理论框架的一些特殊性质,包括能动量张量中的反对称结构以及赝规范变换性质等; 3)在Bjorken和Gubser膨胀体系中的解析解及其对于重离子碰撞物理的意义.     

谐振子系统的量子-经典轨道、Berry相及Hannay角

从量子-经典轨道和几何相两方面, 研究了二维旋转平移谐振子系统的量子-经典对应. 通过广义规范变换得到了Lissajous经典周期轨道和Hannay角. 另外, 使用含时规范变换解析推导了旋转平移谐振子系统Schrödinger方程的本征波函数和Berry相, 得出结论: 原规范中的非绝热Berry相是经典Hannay角的-n倍. 最后, 使用SU(2)自旋相干态叠加, 构造一稳态波函数, 其波函数的概率云很好地局域于经典轨道上, 满足几何相位和经典轨道同时对应.     

1+1维非线性σ模型的BRST变换的等价性和Ward恒等式

在依据Dirac约束规范理论和作推广后的条件下,导出了规范生成元,推导出了1+1维O(3)非线性σ模型的一般条件(β≠0)下的BRST变换,给出了其BRST变换与Dirac规范变换的等价关系,得到了鬼场的新的一般对易关系,且其一般参数β为零时就回到通常的鬼场的对易关系.并由规范生成元导出了BRST荷,进而完成了此模型的一种BRST量子化.还在此基础上进一步导出了此系统的Green函数生成泛函、连通Green函数生成泛函和正规顶角生成泛函,获得了3种不同的Ward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.     

具有半单李代数结构的线性非自治量子系统的精确解

给出了对于具有半单李代数结构的线性量子系统求其精确解的代数动力学方法. 这个方法通过一系列规范变换,把哈密顿量逐步简化为Cartan算子的函数. 规范变换的系数由一组常微分方程确定,Schrodinger方程的完全解通过这组规范变换的逆变换得到.与此同时,还可以得到一组与时间有关的动力学不变量. 作为例子,又具体求解了一个SU(3)模型.     

电磁场矢势和标势从洛伦兹势变换到库仑势的证明

电磁场的标势φ与矢势A具有规范不变性,可以进行规范变换.证明了洛伦兹势经过规范变换成为库仑势.     

预平衡反应多步复合理论和复合核反应理论的统一表示

将Feshbach-Kerman-Koonin(FKK)量子多步复合(MSC)理论推广至核子自旋为1/2,靶核自旋任意,在j-j表象严格处理角动量耦合,得到自旋为1/2的FKK-MSC公式.进一步用光学模型吸收代替门态强度函数,以及用复合核衰变宽度代替平衡态的逃逸宽度,给出了FKK-MSC理论与复合核反应Hauser-Feshbach模型(HFM)的一个统一表达式.这一公式将MSC和HFM与光学模型相联系,对核反应给出自洽和一致的描述.利用上述工作对一些典型的核反应实验进行了初步地分析,计算结果合理,与实验数据符合尚好.     

随时间变化磁场中自旋演化的求解新方法

采用粒子自旋角动量的两个独立谐振子实现和含时规范变换方法,得到不同空间位形的时变磁场中粒子的自旋态,并指出作旋转波近似,即忽略含时快变反共振项的物理原因。本文所用的新方法可应用于其它一些量子系统。     

自旋S=1淬灭键稀释蜂窝格子伊辛模型

本文提出一种新的缀饰方法,将交换作用参数处在子空间exp(K)cosh(J)=1的自旋S=1淬灭键稀释伊辛模型映象到混合自旋淬灭座稀释缀饰格子系统。对此混合自旋缀饰系统,应用退火模型近似求得自旋S=1淬灭键稀释蜂窝格子伊辛系统的临界温度、磁化强度与键浓度之间的解析关系。 关键词：     

Gravity and Spin Forces in Gravitational Quantum Field Theory

In the new framework of gravitational quantum field theory(GQFT) with spin and scaling gauge invariance developed in Phys. Rev. D 93(2016) 024012-1, we make a perturbative expansion for the full action in a background field which accounts for the early inflationary universe. We decompose the bicovariant vector fields of gravifield and spin gauge field with Lorentz and spin symmetries SO(1,3) and SP(1,3) in biframe spacetime into SO(3) representations for deriving the propagators of the basic quantum fields and extract their interaction terms. The leading order Feynman rules are presented. A tree-level 2 to 2 scattering amplitude of the Dirac fermions, through a gravifield and a spin gauge field, is calculated and compared to the Born approximation of the potential. It is shown that the Newton's gravitational law in the early universe is modified due to the background field. The spin dependence of the gravitational potential is demonstrated.     

Gravity and Spin Forces in Gravitational Quantum Field Theory

In the new framework of gravitational quantum field theory (GQFT) with spin and scaling gauge invariance developed in Phys. Rev. D 93 (2016) 024012-1, we make a perturbative expansion for the full action in a background field which accounts for the early inflationary universe. We decompose the bicovariant vector fields of gravifield and spin gauge field with Lorentz and spin symmetries SO(1,3) and SP(1,3) in biframe spacetime into SO(3) representations for deriving the propagators of the basic quantum fields and extract their interaction terms. The leading order Feynman rules are presented. A tree-level 2 to 2 scattering amplitude of the Dirac fermions, through a gravifield and a spin gauge field, is calculated and compared to the Born approximation of the potential. It is shown that the Newton's gravitational law in the early universe is modified due to the background field. The spin dependence of the gravitational potential is demonstrated.     

Magnetic properties of the quantum spin-$\frac{1}{2}$ XX diamond chain: the Jordan-Wigner approach

The Jordan-Wigner transformation is applied to study magnetic properties of the quantum spin- \frac12\frac{1}{2} XX model on the diamond chain. Generally, the Hamiltonian of this quantum spin system can be represented in terms of spinless fermions in the presence of a gauge field and different gauge-invariant ways of assigning the spin-fermion transformation are considered. Additionally, we analyze general properties of a free-fermion chain, where all gauge terms are neglected and discuss their relevance for the quantum spin system. A consideration of interaction terms in the fermionic Hamiltonian rests upon the Hartree-Fock procedure after fixing the appropriate gauge. Finally, we discuss the magnetic properties of this quantum spin model at zero as well as non-zero temperatures and analyze the validity of the approximation used through a comparison with the results of the exact diagonalization method for finite (up to 36 spins) chains. Besides the m = 1/3 plateau the most prominent feature of the magnetization curve is a jump at intermediate field present for certain values of the frustrating vertical bond.     

Absence of spontaneous magnetization in spin systems with competing interactions

It is rigorously proved that spontaneous magnetization is absent in disordered spin systems if the strength of interaction is distributed symmetrically around a vanishing mean value, as a consequence of local gauge symmetry. This result is extended also to asymmetric distributions. A comment is made on gauge symmetry and frustration in quantum spin systems.     

Spin Hall effects for cold atoms in a light-induced gauge potential

We propose an experimental scheme to observe spin Hall effects with cold atoms in a light-induced gauge potential. Under an appropriate configuration, the cold atoms moving in a spatially varying laser field experience an effective spin-dependent gauge potential. Through numerical simulation, we demonstrate that such a gauge field leads to observable spin Hall currents under realistic conditions. We also discuss the quantum spin Hall state in an optical lattice.     

Quantum Spin Hall Effect in a Triple-Well Quantum Dot System

A scheme for generating a quantum spin Hall effect for an ensemble of electrons trapped in a triple-well quantum dot system is proposed. Light-induced effective spin-dependent gauge potential and gauge filed are both given in a real Gaussian pulses space. In our scheme, the spin Hall effect can be demonstrated by electronic population without spin-orbit coupled interaction in the absence of any magnetic fields.     

Coulombic quantum liquids in spin-1/2 pyrochlores

We develop a nonperturbative gauge mean field theory (gMFT) method to study a general effective spin-1/2 model for magnetism in rare earth pyrochlores. gMFT is based on a novel exact slave-particle formulation, and matches both the perturbative regime near the classical spin ice limit and the semiclassical approximation far from it. We show that the full phase diagram contains two exotic phases: a quantum spin liquid and a Coulombic ferromagnet, both of which support deconfined spinon excitations and emergent quantum electrodynamics. Phenomenological properties of these phases are discussed.     

Spin Hall effect induced by a gravitational field

The experiment by Collela et al. (1975) [1] evidenced in a striking manner how the gravitational field appears in quantum mechanics. Within the modern framework of gauge theories, one can ascribe such effect as due to gauge fields originated from fundamental symmetries of spacetime: local transformations of the Lorentz-Poincaré group. When this gauge principle is applied to the Dirac equation, we obtain kinematical correlations between the gravitational field and the spin of the particles. The phenomenon is similar to the spin Hall effect found in condensed matter systems, although much smaller in magnitude. Actual measurements may require highly precision interferometric techniques with spin-polarized neutrons.     

Maximal symmetry and mass generation of Dirac fermions and gravitational gauge field theory in six-dimensional spacetime

The relativistic Dirac equation in four-dimensional spacetime reveals a coherent relation between the dimensions of spacetime and the degrees of freedom of fermionic spinors. A massless Dirac fermion generates new symmetries corresponding to chirality spin and charge spin as well as conformal scaling transformations. With the introduction of intrinsic W-parity, a massless Dirac fermion can be treated as a Majorana-type or Weyl-type spinor in a six-dimensional spacetime that reflects the intrinsic quantum numbers of chirality spin. A generalized Dirac equation is obtained in the six-dimensional spacetime with a maximal symmetry. Based on the framework of gravitational quantum field theory proposed in Ref. [1] with the postulate of gauge invariance and coordinate independence, we arrive at a maximally symmetric gravitational gauge field theory for the massless Dirac fermion in six-dimensional spacetime. Such a theory is governed by the local spin gauge symmetry SP(1,5) and the global Poincar′e symmetry P(1,5)= SO(1,5) P~(1,5) as well as the charge spin gauge symmetry SU(2). The theory leads to the prediction of doubly electrically charged bosons. A scalar field and conformal scaling gauge field are introduced to maintain both global and local conformal scaling symmetries. A generalized gravitational Dirac equation for the massless Dirac fermion is derived in the six-dimensional spacetime. The equations of motion for gauge fields are obtained with conserved currents in the presence of gravitational effects. The dynamics of the gauge-type gravifield as a Goldstone-like boson is shown to be governed by a conserved energy-momentum tensor, and its symmetric part provides a generalized Einstein equation of gravity. An alternative geometrical symmetry breaking mechanism for the mass generation of Dirac fermions is demonstrated.