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.     

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.     

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：     

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：     

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：     

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：     

SU(2)格点规范理论一种新作用量的弦张力的Monte Carlo计算

在10⁴格点上我们对作用量为S_p=sin1-sin(1/2)TrU_p的SU(2)格点规范系统进行了Monte Carlo模拟,计算了弦张力σ和标度常数Δ₀²之比。计算还表明,元格的平均内能和比热峰对于格点体积的变化来说是稳定的。 关键词：     

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.     

VARIATIONAL ANALYSIS OF THE PHASE STRUCTURE OF THE SU(3) LATTICE GAUGE THEORY WITH A MIXED FUNDAMENTAL-ADJOINT ACTION

The variational analysis of the phase structure of the SU(3) lattice gauge theory with a mixed fundamental-adjoint action is presented. All transitions are found to be the first order. The shape of the first order transition line is roughly consistent with the one given by Monte Carlo method.     

THE MULTISYNCHRO-SPHERICAL SOLUTIONS OF THE SU(N)GAUGE THEORY

We study the monopole solutions of the SU(N) gauge group systematically,generalize the current synchro-spherical symmetrical monopole to the multi synchro-spherical symmetrical case,and give the complete classification of the monopole so-lutions.As examples,we have calculated the SU(3) and SU(4) monopoles in detail,and discuss some problems such as angular momenta and topological quantum num-bers.     

MODIFIED MK TRANSFORMATION OF SU(2) GAUGE THEORY

By using the modified MK renormalization transformation, the phase boundaries and renormalization trajectories of the couplings for an SU(2) single plaquette action with variable compments of spin 1/2 and spin 1 in the whole coupling parameter space are obtained. The results are discussed.     

ANALYTIC CALCULATION FOR GLUON CONDENSATION IN SU (2) LATTICE GAUGE THEORY

Using cumulant expansion method, we obtain gloun condensation for pure SU (2) gauge theory analytically.     

UNITARY TRAPJSFORMATIOPJS IN LATTICE GAUGE THEORY WITH FEPMIONS AND THE MESON SPECTRUM

The Hamiltonian of lattice gauge theory with fermions is diagonalized in the one-link approximation and the meson spectrum of SU(N) theory with one flavor is derived.     

ANALYTIC STUDY OF su(3) LATTICE GAUGE THEORY

The variational-cumulant expansion method has been extended to the case of lattice SU(3) Wilson model.The plaquette energy as an order parameter has calculated to the 2nd order expansion.No 1st order phase transition in the d=4 case is found which is in agreement with the monte Carlo results,and the 1st order phase transition in the d=5 case is clearly seen.The method can be used in the study of problems is LGT with SU(3) gauge group.     

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.     

CN REALIZATION OF THE CHIRAL SYMMETRY IN THE LATTICE GAUGE THEORY CONTAINING THE U(I) CHIRAL GAUGE FIELD

We investigate the lattice gauge theory with a gauge group UxV(1) where U is a non-Abelian group and V(1) is a chiral Abelian group.In the strong coupling approximation for the U gauge field we find that the V(1) chiral symmetry is realized through parity doublets of composite fermions for strong V(1) coupling and that it is spontaneousely broken through a techni color-like mechanism for weak V(1) coupling.     

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.     

A VARIATIONAL METHOD IN LATTICE GAUGE THEORY BASED ON HÖLDER INTEGRAL INEQUALITY

A variational method based on Hölder integral inequality is presented. Taking the parameters in integral inequality as variational parameters, we can calculate the free energy in lattice gauge system. The plaquatte energy of Z₂ 、U(1)、 SU(2) gauge system is found and consistent with that given by Monte Carlo method. But, the higher phase transitions for U(1), SU(2) gauge systems are not found.     

THE MASS GAP IN 2+1 DIMENSIONAL SU(3) LATTICE CAUGE THEORY

We present a variational calculation of C=+1 and C=－1 glueball masses in 2+1 dimensional SU(3) lattice gauge theory using a Hamiltonian in which the ground state is exactly known.In the range 0<1/g²≤6,we obtain good scaling behaviour am₊=36.1g² and am_－=5.98g².     

ON THE ANALYTICAL STUDY IN LATTICE GAUGE FIELD THEORY

The relation between the saddle point approximation and the action variational method in the lattice gauge field theory is discussed. It is expounded that in the thermodynamical limit by using a trial action composed of mean fields, the variational approach leads to the results as well as the higher order corrections obtained in the saddle point approximation. It is also pointed out that order by order corrections to the variational approach can be worked out systematically in an improved variational approach.