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.     

无费密子格点规范理论几种新作用量的探讨

我们提出了几种无费密子格点规范理论的新作用量形式,证明了它们符合Wilson对格点作用量提出的条件,讨论了它们与几种常用的作用量间的关系。并推导了在使用新作用量时Wilson圈满足的Schwinger-Dyson方程,证实了当N→∞时,E-K模型中的Schwinger-Dyson方程和标准格点模型相同。 关键词：     

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.     

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.     

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 FOKKER-PLANCK EQUATiON AND THE SCHWI NGER-DYSON EQUATION IN LATTICE GAUGE THEORY

The stochastic quantization in Lattice Gauge Theory (LGT) is discussed by using Langevin equations and Fokker-Planck equations. It is shown that the evolution equation in stochastic process reduces to Schwinger-Dyson equation when lattice system reaches equilibrium.     

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.     

A SELF-DUAL GAUGE THEORY

An Abelian gauge theory enriched with monopoles is shown to be self-dual and can be transformed into a self-dual Abelian Higgs theory.     

THE PERTURBATION EXPANSION OF THE QUANTIZED COMPOSITE FIELD THEORY AND GAUGE INVARIANCE

In this paper we introduce the concept of "same order" in the perturbution expansion of the quatized composite field theory which is different from single particle theory. For example, in the case of Q. E. D., "same order" is defined by means of a coupling constant, but here it closely relates the operators occuring in the B. S. equations. Feymann graphs of the "same order" are defined for different kinds of transitions in the composite field theory. Finally, we prove that guage invariance is a natural result as long as all "same order" Feymann graphs are calculated for an electromagnetic transition between composite particles.     

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.     

THE VACUUM OF LATTICE GAUGE THEORY WITH FERMIONS AND SPONTANEOUS CHIRAL SYMMETRY BREAKING*

The vacuum structure of lattice gauge theory with femicns is studied by the variational method.The fermion condensate <ψψ> is given as a function of l/g².     

A REAL-SPACE RENORMALIZATION-GROUP ANALYSIS FOR Z2 LATTICE GAUGE THEORY COUPLED TO A HIGGS FIELD

We present a real-space renormalization-group analysis for Z₂ lattice gauge theory coupled to a Higgs field in four dimension,the results show a phase diagram in which the Higgs and confined region are smoothly connected.     

THE DECAY ρ→ππ IN LATTICE GAUGE THEORY

The hadronic decays are studied by using an improved Hamiltonian including 2-link interactions. We find that the formulation is effective for studying hadronic decays as well as mass spectrum. In the intermediate coupling region,the decay width of ρ meson is found to be of the right order of magnitude.     

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.     

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.     

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.     

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：     

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：     

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.     

MONTE CARLO STUDY OF MANTON'S ACTION FOR FOUR-DIMENSIONAL SU(5) LATTICE GAUGE THEORY

The feature of Manton's lattice action in the SU(5) four-dimensional lattice gauge theory is investigated by means of Monte Carlo simulation. A rather smooth curve of the internal energy is obtained, no discontinuity in the average action perplaquette is found in opposition to the resultes of usually adopted Wilson's action. An evidence of a higher order phase transition with Manton's action is also found.