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.     

广义QCD中正则形式的Ward恒等式

导出了高阶微商奇异拉氏量系统正则形式的Ward恒等式并将其应用于广义色动力学(QCD),得到了广义QCD中规范场和鬼场正规顶角间的某些新关系,它们有别于BRS不变性所导致的结果;还得到了广义QCD中的PCAC和AVV顶角的Ward恒等式.     

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.     

高阶微商系统Dirac猜想的一个反例

由扩展正则作用量导出了高阶微商奇异Lagrange量系统的扩展正则Noether恒等式.从广义约束Hamilton系统相空间中对称性分析，给出高阶微商系统Dirac猜想的一个反例. 用正则Noether定理、 正则Noether恒等式和扩展正则Noether恒等式说明在此反例中Dirac猜想失效, 讨论中没有将约束线性化. 关键词： 高阶微商系统 约束Hamilton系统 正则对称性 Dirac猜想     

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.     

正则形式的SU(N)规范理论的约束关联动力学(Ⅱ)规范理论的约束条件

用Dirac理论分析SU(N)规范理论的约束及量子化问题.用代数动力学观点处理规范不变性、高斯定律与Ward恒等式.并运用关联动力学中的守恒定律思想,把与剩余规范不变性相联系的高斯定律和Ward恒等式转化成守恒定律与初值问题.     

正则Ward恒等式和Abel规范理论中动力学质量的产生

文中基于约束Hamilton系统理论用Faddeev-Senjanovic路径积分量子化方法,重新讨论了Cornwall-Norton和Jackiw-Johnson模型的量子化,导出了这两个系统的正则Ward恒等式,利用导出的正则Ward恒等式,得到了包括费米子和束缚态的质量谱.所得的结果与其他方法导出的结果相同     

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.     

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.     

N=2超对称大统一理论中规范破缺注记

本文讨论了用N=2超对称有限理论建立现实大统一模型的可能性. 发现规范对称自发破缺和超对称破缺是可以实现的, 但在夸克轻子质量问题上遇到困难.     

Higgs机制与变换

Higgs机制在量子场论中作用十分重要 ,它使规范场有了质量 .本文不引入协变导数 ,通过一类变换 ,得到了规范场的质量     

New variable formalism of higher derivative gravity

Starting from the O(4) field variables, which are the euclidean version of the O(3,1) Lorentz group, a new formulation of higher derivative gravity is given in an SU(2) gauge invariant form. The dynamics of the higher derivative gravity is therefore determined by this SU(2) gauge theory proposed here and it can be seen that its vacuum is in a spontaneously broken phase. The Planck mass is considered to be generated as a result of this symmetry breaking.     

One-loop induced topological term in QED3

We consider the 2+1 dimensional massive QED and discuss the induced topological term in the one-loop level by using the higher derivative regularization. We show that the higher derivative regularization, which manifestly preserves the parity invariance when the fermion mass vanishes, automatically leads to a nonvanishing topological term in low energies. Although this higher derivative regularization formally violates the local gauge invariance, we propose a systematic way to recover the gauge invariance by adding local counter terms dictated by Ward-Takahashi identities. In practical applications, this regularization is interesting in connection with the discussion of the dynamical origin of the quantum Hall effect.     

Chiral Schwinger model with a Podolsky term at finite temperature

We study an exactly solvable two-dimensional model which mimics the basic features of the standard model. This model combines chiral coupling with an infrared behavior which resembles low energy QCD. This is done by adding a Podolsky higher-order derivative term in the gauge field to the Lagrangian of the usual chiral Schwinger model. We adopt a finite temperature regularization procedure in order to calculate the non-trivial fermionic Jacobian and obtain the photon and fermion propagators, first at zero temperature and then at finite temperature in the imaginary and real time formalisms. Both singular and non-singular cases, corresponding to the choice of the regularization parameter, are treated. In the nonsingular case there is a tachyonic mode as usual in a higher order derivative theory, however in the singular case there is no tachyonic excitation in the spectrum.     

The derivative expansion of the fermion number current

The fermion number current is evaluated to leading order in the derivative expansion for chiral fermions in the background of arbitrary Higgs and chiral gauge fields. This current is given by the gauge topological current plus a total divergence term. The total divergence term is absent in Weinberg-Salam theory with one scalar Higgs doublet, even for an arbitrary mass matrix, but appears when several Higgs doublets are present.     

Massive spin 3/2 theories in 3 dimensions

Topologically massive spin 3/2 theory in 3 spacetime dimensions, which is gauge invariant and involves second derivatives, is shown to be equivalent to the normal gauge variant first derivative massive Rarita-Schwinger model. The equivalence persists in arbitrary background geometries. In the particular anti-de Sitter space whose cosmological constant is minus the mass squared, the model effectively behaves like the massless theory in flat space: its degree of freedom disappears.     

Loop variables and gauge invariant exact renormalization group equations for (open) string theory

An exact renormalization group equation is written down for the world sheet theory describing the bosonic open string in general backgrounds. Loop variable techniques are used to make the equation gauge invariant. This is worked out explicitly up to level 3. The equation is quadratic in the fields and can be viewed as a proposal for a string field theory equation. As in the earlier loop variable approach, the theory has one extra space dimension and mass is obtained by dimensional reduction. Being based on the sigma model RG, it is background independent. It is intriguing that in contrast to BRST string field theory, the gauge transformations are not modified by the interactions up to the level calculated. The interactions can be written in terms of gauge invariant field strengths for the massive higher spin fields and the non-zero mass is essential for this. This is reminiscent of Abelian Born–Infeld action (along with derivative corrections) for the massless vector field, which is also written in terms of the field strength.     

Effective action for the standard model with large Higgs mass

The covariant derivative expansion of the one-loop effective action is briefly reviewed, and applied to the problem of calculating the heavy Higgs effects in the standard Glashow-Weinberg-Salam model. All terms which grow with the Higgs mass M_H at one loop are found. The result of this calculation is used to find the dependence of the gauge boson mass ratio ϱ on M_H, and also to estimate the size of corrections to W and Z scattering theorems.     

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.     

Covariant derivative on non-linear fiber bundles

A gauge field is usually described as a connection on a principal bundle. It induces a covariant derivative on associated vector bundles, sections of which represent matter fields. In general, however, it is not possible to define a covariant derivative on non-linear fiber bundles, i.e. on those which are not vector bundles. We definelogarithmic covariant derivatives acting on two special non-linear fiber bundles — on the principal bundle and on the local gauge group bundle. The logarithmic derivatives map from sections of these bundles to the sections of the local gauge algebra bundle. Some properties of the logarithmic derivatives are formulated.