STRONG INTERACTION AND CHIRAL GAUGE FIELD

The concept of e^{iα（x）γ_s} local gauge transformation is introduced in this article. The chiral gauge invariant Lagrangian is given. The relationship between chiral gauge field and strong interaction is also discussed. In a special condition, we obtain the effective Lagrangian for V-A type strong interaction.     

CONFINEMENT PROPERTIES OF PURE GAUGE FIELCS ON COSET SPACE OF THE NON-ABELIAN CHIRAL GROUP

In this paper the method of lattlce gauge theories is applied to the investigation of the effect of coset pure gauge fields of the non-Abelian chiral group on the confinement properties of a system. In particular, the current-current propagator of the coset G/H=SU(2)_L×(2)_r/SU(2) model is calculated. Then it IS found that the pure gauge fields-on coset space only offer a perimeter law factor which does not change the confinement properties of a physical system.     

CONFINEMENT PROPERTIES OF THE PURE GAUGE FIELDS ON COSET SPACE OF AN ABELIAN CHIRAL GROUP

In this paper the lattice current-current propagator is calcdlated and the influence of coset pure gauge fields of an abelian chiral group G=U₁×U₁⁵ on confinement properties of a quark system is discussed by virtue of the Wilson's criterion in lattice gauge theory. When subgroup H is U₁, the coset pure gauge fields only contribute a perimeter law factor to the current current propagator which has no influence on confinement properties of the system. When subgroup H is U_s, the coset puregauge fields have no influence on wnfinement properties of the system either.     

CONFINEMENT PROPERTIES OF THE PURE GAUGE FIELDS ON COSET SPACE OF AN ABELIAN CHIRAL GROUP

In this paper the lattice current-current propagator is calculated and the influence of coset pure gauge fields of an Abelian chiral group G=U₁×U⁵ on confinement properties of a quark system is discussed by virtue of the Wilson's criterion of lattice gauge theory. When subgroup H is U₁, the coset pure gauge fields only contribute a perimeter law factor to the current-current propagator which has no influence on confinement properties of the system. When subgroup H is U⁵, the coset pure gauge fields also have no influence on confinement properties of the system.     

Proof of chiral symmetry breaking in strongly coupled lattice gauge theory

We study chiral symmetry in the strong coupling limit of lattice gauge theory with staggered fermions and show rigorously that chiral symmetry is broken spontaneously in massless QED and the gauge-invariant Nambu-Jona-Lasinio model if the dimension of spacetime is at least four. The results for the chiral condensate as a function of the mass imply that the mean-field approximation is an upper bound for this observable which becomes exact as the dimension goes to infinity. For the model with gauge groupU(N),N=2,3,4, we prove that chiral long-range order exists at zero mass in four or more dimensions. Address after August 1991: Mathematics Department, University of British Columbia, Vancouver, Canada V6T1Y4     

重整化群变换应用于U(1)规范理论的定量分析

在Migdal及Migdal-Kadanoff重整化群变换方案中,我们导出了U(1)格点规范理论的强耦合(高温)近似和弱耦合(低温)近似,同时还得到了包括中间耦合区的数值结果。上述结果与严格的强耦合展开、弱耦合展开以及Monte-Carlo模拟结果进行了比较。 关键词：     

THE GAUGE OPERATORS FOR PSEUDOSCALAR FIELDS AND THE BAKER-HAUSDORFF FORMULA

In this paper, we present the explicit expressions of the gauge operators for pseudoscslar fields in a gauge theory coupled vector and axial-vector fields with the aid of the method of operator algebras.The gauge operators of the pure gauge field theory under the chiral group SU(N)×SU(N) are also presented. P9oreover, the explicit expression of the Baker-Hausdorff formula is obtained for a special case and the general situation is discussed.     

THE GAUGE INVARIANT WESS-ZUMINO ACTION FUNCTIONAL,CHIRAL ANOMALIES AND TOPOLOGY

The gauge invariant Wess-Zumino action functional in 2n dimensional space is obtained by properly constructing the manifestly gauge invariant (2n+1)-forms which satisfy the Abelian anomalous Ward identity in 2n+2 dimensional space. Apart from its simplicity, directness, the construction clearlu embodies the connections between the gauge invariant Wess-Zumino action functional, cniral anomalies and topology.     

LATTICE FORMULATION OF THE PURE GAUGE FIELDS ON COSET SPACE

In this paper we construct the lattice formulation of the pure gauge fields in a coset space in the cases of a group G with non-trivial topological property and of a chiral group G, and present a local gauge invariant action of a quark system on a fourdimensional Euclidean space lattice, which has the continuum limit as usual. For non-chiral group with trivial topological property, it is shown that the coset pure gauge fields have no influence on the confinement properties of the quark system by calculating latt-ice current-current propagztor when the coset pure gauge fields are retained manifest1y.     

LATTICE FORMULATION OF THE PURE GAUGE FIELDS ON COSET SPACE

In this paper we construct a lattice formulation of the pure gauge fields on a coset space in the cases of a group G with non-trivial topological property and of a chiral group G, and present a local gauge invariant action of a quark system on a four-dimensional Euclidean space lattice, which has the continuum limit as usual. For non-chiral group with trivial topological property, it is shown that the coset pure gauge fields have no influence on the confinement properties of the confinement properties of the quark system by calculating lattice current-current propagator when the coset pure gauge fields remain manifest.     

A numerical study of lattice QED with dynamical fermions

Using the pseudo-fermion method U(1) lattice gauge theory with dynamical staggered fermions is studied. The plaqette energy, the chiral order parameter and the Polyakov line have been measured. With fermions of mass 0.20 and 0.25 a phase transition is observed, separating the strong coupling regime from a phase where chiral symmetry is restored.     

STRING THEORY WITH THREE FAMILIES OF CHIRAL FERMIONS

A heterotic string theory is constructed by compactifying directly from 26 to 4 dimensions via a smooth manifold T²²/G. In the low energy limit, there are three families of chiral fermions with exactly the same quantum numbers as thatin the standard supersymmetric SU(3)×SU(2)×XU(1) model. They couple to supergravity and supergauge fields with the gauge symmetry SU(3)_F×SU(3)_c×SU(3)_L×U(1)_YR×U(1)_I3R.     

关于非阿贝耳规范群的对偶荷问题——一个对单磁荷的讨论

从规范场的积分定义出发,应用一个类似于在紧致流形上建立起来的微分几何定理——Gauss-Bonnet定理——的公式得到了普遍的规范荷与对偶荷的共轭关系。电子荷与单磁荷就是这种共轭关系的一例。当规范群为SO(3),含有U(1)群作为其不变子群时,无需引入任何关于奇异弦概念或任何自发破缺对称性的机制,我们自然地得到’t Hooft的单磁荷解。     

The anomaly cancellation mechanism in N=1, D=4 supergravity and distorted supergravity algebra with Chern-Simon forms

A mechanism is exhibited which ensures that N=1, D=4 new minimal supergravity is free of Lorentz×U(1) anomalies, for any coupling to matter, although it contains an abelian chiral gauge field. This is achieved through the determination of a new supergravity algebra characterized by the presence of a U(1)×Lorentz Chern-Simon form in the field strength of a two-form gauge field. Our analysis provides therefore an example in which Chern-Simon type interactions do occur, while preserving local supersymmetry.     

Isospin breaking of the narrow charmonium state of Belle at 3872 MeV as a deuson

We investigate the continuum limit of a compact formulation of the lattice U(1) gauge theory in 4 dimensions using a nonperturbative gauge-fixed regularization. We find clear evidence of a continuous phase transition in the pure gauge theory for all values of the gauge coupling (with gauge symmetry restored). When probed with quenched staggered fermions with U(1) charge, the theory clearly has a chiral transition for large gauge couplings. We identify the only possible region in the parameter space where a continuum limit with nonperturbative physics may appear.     

各级微扰展开下自发破缺的规范无关性、么正性及可重整性

用微扰论展开明显地讨论了标粒子与规范场矢粒子自发破缺Abel模型,发现在各种可重整规范下同阶各费曼图的内线非物理分量贡献的规范有关部分只与外线的质壳外部分互相依存。在质壳上只剩下物理分量的贡献,亦即转化成了么正规范。这样就明显地验证了么正规范与可重整规范在质壳上的全同,从而说明可重整规范是么正的,以及么正规范下怎样会出现剩余发散,为何剩余发散必然相消,揭穿了么正规范的隐藏可重整性。     

FURTHER DISCUSSIONS OF THE EXACT GAUGE COUPLING β FUNCTION IN SUPERSYMMETRIC YANG-MLLLS THEORIES

The exact gauge coupling β function in the N-extended pure supersymmetric Yang-Mi11s (SYM) theories is extended to arbitraru gauge group and the exact β function in N=2 SyM theories with N=2 matter multiplets is obtained. Its vanishing in the latter cases is explicitly checked at two-loop level.     

Domain wall fermions with Majorana couplings

We examine the lattice boundary formulation of chiral fermions with either an explicit Majorana mass or a Higgs-Majorana coupling introduced on one of the boundaries. We demonstrate that the low-lying spectrum of the models with an explicit Majorana mass of the order of an inverse lattice spacing is chiral at tree level. Within a mean-field approximation we show that the systems with a strong Higgs-Majorana coupling have a symmetric phase, in which a Majorana mass of the order of an inverse lattice spacing is generated without spontaneous breaking of the gauge symmetry. We argue, however, that the models within such a phase have a chiral spectrum only in terms of the fermions that are singlets under the gauge group. The application of such systems to non-perturbative formulations of supersymmetric and chiral gauge theories is briefly discussed.     

Fateev-Zamolodchikov量子自旋链的潜藏定域规范不变性

详细研究了自旋为1的Heisenberg XXZ模型(Fateev-Zamolodchikov模型)的潜藏定域规范不变性。发现与自旋为1/2的情形相类似,该模型允许AbelU(1)规范交换,且其能谱在规范变换下保持不变,而其本征矢却与规范变换明显相关。