THE MC CALCULATION OF MASS GAP IN 2+1 DIMENSIONAL SU(2) LATTICE GAUGE THEORY

By combining Monte Carlo method and variational method,we calculate the mass gap of SU(2) lattice gauge theory in 18*18 lattice of 2+1 dimensions by means of the icosaheral subgroup (Y120) using a hamiltonian of which the ground state is exactly known.In the range 0<1/g²,we obtain the results which are in good agreement with analytical calculation of SU(2) group.The scaling behaviour of mass gap am=2.3g² is confirmed.     

THE MASS GAP IN 2+1 DIMENSIONAL SU(2) LATTICE GAUGE THEORY

A variational calculation of the mass gap in 2+1 dimensional SU(2) lattice gauge theory by using a Hamiltonian with the ground state being exactly known is made.In the range 0≤1/g²≤7,a good scaling behaviour am=2.28g² is obtained,which is in agreement with weak-coupling perturbation theory.     

THE VARIATIONAL CALCULATION OF MASS GAP IN 2+1 DIMENSIONAL SU(2) LGT

A variational calculation of the mass gap in 2+1 dimensional SU(2) lattice gauge theory by using a Hamiltonian which possesses exact ground state and correct continuum limit is made.In the range 1.3≤1/g²≤7,a good scaling behaviour am=2.28g² is obtained,which is in agreement with weak-coupling perturbation theory and the results obtained by another Hamiltonian which does not possess correct continuum limit.     

耦合常数小于1时SU(2)格点规范理论的质量隙及β函数计算

通过改变格点规范理论的作用量,我们把Monte Carlo计算的“窗口”移到了耦合常数小于1的区域。这就提供了在较弱耦合下作Monte Carlo计算的另一种途径。在3.9≤β≤4.7区域内,在10⁴格点上,我们计算了SU(2)规范的重整化群β函数及质量间隙,观察到类似于Wilson作用量的标度行为,估算出M≈(3.9±1.0)σ^1/2。 关键词：     

THE VARIATIONAL CALCULATION OF MASS GAP IN 2+1 DIMENSIONAL U(1) LGT

We present a variational calculation of 0^+－ and 0⁺⁺ glueball masses in 2+1 dimensional U(1) lattice gauge theory by using a Hamiltonian which possesses exact ground state and correct classical continuum limit.In deep weak coupling region,we obtain that am(0^+－) decreases with 1/g² exponentially and am(0⁺⁺)=2.78g².     

SU(2)格点规范理论中的重夸克相互作用力及势的计算

本文用Monte Carlo方法对四维对称格点规范理论中具有较好标度性行为的单元格EXP作用量计算了重夸克-反夸克势。计算中利用了重整化群处理方法和SU(2)群的正二十面体子群近似。计算结果与维象的弦理论给出的库仑势加线性势的形式一致。 关键词：     

VARIATIONAL TREATMENT WITH THE THIRD ORDER CORRECTIONS FOR SU(2) LATTICE GAUGE THEORY

The variational method in Lagrangian formalism in lattice gauge theory in cumulant expansion is discussed. For SU(2) pure gauge Wi1son model to the third order corrections we show that there is no phase transition in four dimensions, but there exists the first order phase transition in five dimensions at β_C=0.838 in agreement with the Monte Carlo results. The physical meaning of higher order corrections is discussed.     

THE IMPROVED HAM1 LTONI AN AND ρ-ω MASS DIFFERENCE IN LATTICE GAUGE THEORY+

We formulate a Hamiltonian theory on the lattice including next-to-nearest neighbor fermion interactions. A canonical transformation is made to induce a momentum-dependent mass term. The meson spectrum is studied by using this Hamiltonian. The current algebra formula for the pion mass is derived. The ρ-ω mass ratio in the intermediate coupling region is in agreement with the experimental value.     

PHASE STRUCTURE OF THE SU(2)-SO(3) LATTICE SYSTEM IN AN IMPROVED VARIATIONAL APPROACH

An improved trial action in the variational approach of the lattice gauge field theory is in-troduced to acquire better lower bound for the convexity Inequality and used to calculate the phase structure of the SU(2)-SO(3) pure gauge system. The improvement is seen in comparing the old and new variational results with that by the Monte Carlo simulation.     

在SU(2)模型中费密子的质量与Rubakov效应

在自发破缺的具有Higgs三重态的SU(2)规范理论中,讨论了同位旋1/2的费密子的质量对费密子-磁单极束缚态的影响。结果表明,当费密子与Higgs场之间的直接耦合趋于零,但狄拉克质量保持固定时,费密子-磁单极束缚态的必要条件必不被满足。这个结果意味着对于SU(2)模型由于狄拉克质量效应,Rubakov效应不存在。 关键词：     

SU(6)对称性理论中的弱相互作用

本文提出了SU(6)对称性理论中的一个弱相互作用中间玻色子方案。基本假定是:(1)中间玻色子归为SU(6)群的不可约表示21;(2)弱流归为正规表示35;从而(3)s波及p波半弱相互作用分别归为表示21中的(3^*,1)部分及表示15中的(3^*,3)部分。则除了△I=1/2规则以外,由此得出的有效超子非轻子作用在s波(宇称破坏)振幅都分给出三个求和规则,在p波(宇称守恒)振幅部分给出一个求和规则,这些关系看来和实验符合得较好。     

用SU(2)的分立子群对SU(2)格点规范新作用量的Monte Carlo 模拟

我们用SU(2)的正二十面体分立子群对SU(2)格点规范理论的正弦作用量与指数作用量进行了Monte Carlo模拟。发现由分立子群本身产生的一阶相变点分别在β_c′≈9.2±0.2和β_c′=6.8±0.2。对方格能量和比热所得的结果与用SU(2)群所得的结果一致。从而证实了对以上两种作用量,用分立子群代替连续群的适用性,为以后进行计算时利用分立子群提供了依据。 关键词：     

VARIATIONAL ANALYSIS OF CUMULANT EXPANSION IN SU(2) LATTICE GAUGE THEORY WITH AN ACTION INCLUDING SIX-LINK LOOPS

By using the cumulant expansion variational method,we study the SU(2) lattice action including six-link loops which satify the request of Symanzik.The average values of the plaquette and six-link loop up to second order approximation are calculated.Our results are consistant with Monte Carlo data.     

群表示论的物理方法(Ⅴ)——SU3?SO3和SU4?SU2×SU2分类基

本文给出了核物理中常用的SU₃?SO₃(f=1—6)和SU₄?SU₂×SU₂波函数在Gelfand表象中的展开系数。 关键词：     

VACUUM OF 2+1 DIMENSIONAL SU(2) LGT WITH FERMIONS AND SPONTANEOUS CHIRAL SYMMETRY BREAKING

By incorporating the exact ground state of pure gauge theory and the variational fermion vacuum state,the vacuum structure of 2+1 dimensional SU(2) LGT with fermions is studied.We calculate the fermion condensate <ψψ>,and obtain a good scaling behavior.

     

Kondo晶格中的超导理论

为解释重费密子超导现象,本文在Kondo晶格中建立了S波和P波超导理论,并在推广的Nambu空间中对f电子和传导电子的杂化作用进行了自洽处理,计算了有关物理量。理论证明:如果认为f电子参与超导,对S波,所得到的超导转变温度与Tachiki等人的结果一致,但比热跃交与他们的不同,本文的结果更合理些;对P波,由Kondo晶格模型描述的重费密子超导系统等效于修正的局域的费密超流体。此外,本文还研究了杂质散射对超导态的影响,并对各种不同的超导态分别得到了出现无能隙超导的条件。 关键词：     

(2+1)维离散型Toda方程的对称性

将文献[1—4]提出的形式级数对称理论推广应用到(2+1)维的离散型Toda方程,得到了二族无穷多广义截断对称。每一族对称构成一个广义W_∞代数,通常的W_∞代数仅是这个代数的子代数。 关键词：     

SU(2)格点规范理论几种不同形式的作用量的Monte Carlo研究

对SU(2)格点规范理论用三种不同于常用形式的作用量进行了Monte Carlo模拟,计算了平均内能和比热。内能曲线都趋向共同的弱耦合极限,都有比热峰标志着临界点。观察到仅由于格点间隔α的高次幂项不同而引起临界点明显漂移的现象。 关键词：     

VARIATIONAL ANALYSIS OF THE SU(3) LATTICE GAUGE THEORY

The variational method in Lagrangian formalism has been applied to investigate the SU(3) Wilson model in lattice gauge theory. No phase transition point has been found. The result is in agreement with that obtained by Monte Carlo simulations.     

ABUNDANT DROMION-LIKE STRUCTURES TO THE (2+1) DIMENSIONAL KdV EQUATION

The abundant generalized dromion structures for the (2+1)-dimensional KdV equation are obtained using the homogeneous balance method. We give not only the general curve soliton which is finite on a curved line and localized apart from the curve, find but also the dromion solutions which can be driven by two perpendicular line soliton and by two non-perpendicular line soliton and by one line soliton and one curve line soliton. Various types of multi-dromion solutions can be constituted by selecting different arbitrary functions of y. The (1+N) dromion obtained by Radha et al.^[3] is only a very special case of our results.