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.     

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.     

Universal weak coupling limit in (2+1)-dimensionalSU(2) lattice gauge theory

Mass gaps and wave functions in (2+1)-dimensionalSU (2) lattice gauge theory (no quarks) are investigated. Starting with lattice Hamiltonians possessing exactly known ground states and the correct naive continuum limit, it is possible to reach the very deep weak-coupling region. Using variational approximation and rescaling all parameters with the help of the dimensionful coupling constantg ², we gain a formulation that is independent of the special choice of the Hamiltonian in the weak-coupling limit. The mass gap can be calculated and a kind of wave function for excited states obtained.     

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.     

Monte Carlo Effective Hamiltonian in 1+1 Dimensional Case'

Using a recently developed Monte Carlo effective Hamiltonian method,we study the low energy physics of 1+1 dimensional quantum mechanical system V(x)=μ²x²+λx⁴(here μ²<0,λ>0),which is similar to Higgs potential in the standard model of unified electroweak theory.Good results of the spectra,wavefunctions and thermodynamical observables are obtained.It shows that the new Monte Carlo Hamiltonian method has potential application to systems with many degrees of freedom and lattice gauge theory.     

SU(2) Lattice gauge theory in (2+1)D

Cluster expansion methods are applied to theSU(2) lattice gauge model in (2+1) dimensions. Strong-coupling series are calculated for the vacuum energy per site, the axial string tension, and the scalar mass gap; while ELCE approximants are used to estimate the string tension beyond its roughening transition. The simple scaling behaviour expected of this super-renormalizable theory is clearly seen, and we estimate that in the continuum limit the string tension σ～(0.14±0.01)g ⁴, while the mass gapM _s ～(2.2±0.25)g ². More accurate Monte Carlo simulations are needed to check the universality between the Hamiltonian and Euclidean versions of this model.     

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.     

Progress in lattice gauge theory

Two topics of lattice gauge theory are reviewed. They include string tension and β-function calculations by strong coupling Hamiltonian methods for SU(3) gauge fields in 3 + 1 dimensions, and a 1/N-expansion for discrete gauge and spin systems in all dimensions. The SU(3) calculations give solid evidence for the coexistence of quark confinement and asymptotic freedom in the renormalized continuum limit of the lattice theory. The crossover between weak and strong coupling behavior in the theory is seen to be a weak coupling but non-perturbative effect. Quantitative relationships between perturbative and non-perturbative renormalization schemes are obtained for the O(N) nonlinear sigma models in 1 + 1 dimensions as well as the range theory in 3 + 1 dimensions. Analysis of the strong coupling expansion of the β-function for gauge fields suggests that it has cuts in the complex 1/g²-plane. A toy model of such a cut structure which naturally explains the abruptness of the theory's crossover from weak to strong coupling is presented. The relation of these cuts to other approaches to gauge field dynamics is discussed briefly.The dynamics underlying first order phase transitions in a wide class of lattice gauge theories is exposed by considering a class of models-P(N) gauge theories - which are soluble in the N → ∞ limit and have non-trivial phase diagrams. The first order character of the phase transitions in Potts spin systems for N #62; 4 in 1 + 1 dimensions is explained in simple terms which generalizes to P(N) gauge systems in higher dimensions. The phase diagram of Ising lattice gauge theory coupled to matter fields is obtained in a $\text{1}\text{N}$ expansion. A one-plaquette model (1 time-0 space dimensions) with a first-order phase transitions in the N → ∞ limit is discussed.     

QUARK MASS RENORMALIZATION IN LATTICE GAUGE THEORY (Ⅱ) BARYON MASS CALCULATION

Using the renormalized quark mass m(g) obtained by fixing the ρ meson mass, we calculate the masses of the baryon states as a function of 1/g² in lattice gauge theory with fermions by variational method. The results are in agreement with experimental values in the range of 1/g² between 0.1 to 0.9.     

Spectral degeneracy of the lattice dirac equation as a function of lattice shape

We investigate the free Dirac equation in 2 + 1 dimensions on square, triangular, and hexagonal lattices. For each lattice the spectrum exhibits a degeneracy not present in the continuum limit. In the square and hexagonal cases there is a 4-fold degeneracy corresponding to 2 independent symmetries of the Hamiltonian; the degeneracy is eliminated by diagonalizing these symmetries and projecting onto the subspace characterized by a particular pair of eigenvalues. For the triangular case the degeneracy is 6-fold, but the naive Hamiltonian does not possess enough symmetry to eliminate the degeneracy. Certain ambiguities in the lattice Hamiltonian are pointed out and by the addition of terms which vanish in the continuum limit, it is cast in a form with sufficient symmetry to remove the degeneracy entirely, just as was done for the hexagonal and square lattices. It is found that after elimination of the spectral degeneracy the Hamiltonians for the hexagonal and triangular lattices are identical. The solutions to these theories are shown to have the correct continuum limit.     

Phase transitions in quantum field theory. I. Phases of the Thirring model

In this series of papers we exhibit and analyse phase transitions in quantum field theory. In this paper we consider the Thirring model. We show that when the interaction becomes sufficiently attractive there is a transition to a vacuum that is ‘dead” in the sense there are no finite energy excitations. Nevertheless the corresponding continuum Green's functions exist. We make this demonstration precise by considering the model on a lattice and constructing the continuum limit explicitly on either side of the critical point. For this we extensively use the connection between the $\text{spin}\text{-}\text{1}\text{2}$x-y-z chain and the lattice model. We also show a new continuum theory with four fermion interactions exists in 1 + 1 dimensions. This theory corresponds to taking the continuum limit of the spin chain in absence of any external magnetic field. Its Hamiltonian differs from that of the Thirring model by addition of fermion number operator with an infinite coefficient and is not renormalizable in the conventional sense. It has more interesting critical properties and a different spectrum.     

Hamiltonian reduction of SU(2) gluodynamics

The Hamiltonian reduction of the Yang-Mills theory with the structure group SU(2) to a nonlocal model of a self-interacting 3 × 3 positive semidefinite matrix field is presented. Analysis of the field transformation properties under the action of the Poincaré group is carried out. It is shown that, in the strong coupling limit, the classical dynamics of a reduced system can be described by the local theory of interacting nonrelativistic spin-0 and spin-2 fields. A perturbation theory in powers of the inverse coupling constant g ^−2/3 that allows calculating the corrections to a leading long-wave approximation is suggested.     

Seventh Order Glueball Mass of the 2+1-D SU(2)LGT in RPA

The random phase approximation (RPA) method and the Feymann-Hellman theorem are used to calculate the seventh order glueball mass of the 2+1-D SU(2) lattice gauge theory. As an approximation, the trial wave function is constructed only by single-hollow graphs. The calculated result of the seventh order glueball mass shows good scaling behavior at the weak coupling region of 1/g²=1.0-1.8(m/e²≈1.20±0.01).     

Generalized Lorentzian triangulations and the Calogero Hamiltonian

We introduce and solve a generalized model of (1+1)D Lorentzian triangulations in which a certain subclass of outgrowths is allowed, the occurrence of these being governed by a coupling constant β. Combining transfer matrix-, saddle point- and path integral-techniques we show that for β<1 it is possible to take a continuum limit in which the model is described by a 1D quantum Calogero Hamiltonian. The coupling constant β survives the continuum limit and appears as a parameter of the Calogero potential.     

Calculation of Vacuum Wavefunction and Mass .Gap from Improved (2+l)-Dimensional SU(2) Lattice Gauge Field Hamiltonian

The truncated eigenvalue equation of SU(N) lattice gauge theory is studied by using improved lattice gauge Hamiltonian with a proper truncation scheme that preserves the continuum limit. The calculations of vacuum state wavefunction and glueball mass of (2+1)-dimensional SU(2) theory up to third order are carried out, the results show the improvement of scaling behavior in deep weak coupling region.     

Contribution of One-Photon Annihilation at ψ(2S) in e+e－ Experiment

The continuum one-photon annihilation at ψ(2S) in e⁺e^－ experiment is studied. Such contributions to the measured final states ωπ⁰ and π⁺π^－ at ψ(2S) mass are estimated by phenomenological models. It is found that these contributions must be taken into account in the determination of branching ratios of ψ(2S)→ωπ0 and ψ(2S)→π⁺π^－, as well as other electromagnetic decay modes. The study reaches the conclusion that in order to obtain the correct branching ratios on these decay modes at BES, at least 10pb^－1of data below the ψ(2S) peak is needed.     

Quark Condensate in Two-Dimensional SU(NC) Lattice Gauge Theory with Massive Wilson Quarks

Using the improved lattice Hamiltonian with massive Wilson quark and the variational method, we study the quark mass m_q and the Wilson parameter r dependences of the quark condensate 〈ψψ〉in the two-dimensional SU(N_C) lattice gauge theory. The numerical results show that when r is given, for N_C=2,3,4,5,6,7, the value of 〈ψψ〉_suba/(gN_C^3/2) decreases as m_q increases. For N_C>3, when m_q is small, 〈ψψ〉_suba/(gN_C^3/2) is almost independent of r; when m_q is large, 〈ψψ〉_suba/(gN_C^3/2)increases with increasing r. Particularly, when m_q→0, our numerical results agree very well with Zhitnitsky's analytical weak coupling result in the continuum, which implys that our numerical results in the case of m_q≠0 are reliable.     

胶体二硫化钼的高压拉曼散射研究

 测量了平均直径为4 μm的胶体二硫化钼粉剂的高压拉曼光谱。实验结果表明,高压下胶体二硫化钼拉曼峰位随压力增大向高波数方向移动,而峰强随压力增大而减小且峰宽展宽。通过对拉曼峰位移随压力变化的曲线分析,得到了胶体二硫化钼的两个振动模式E¹_2g和A_1g的模式格林爱森常数值。     

The vacuum energy of QED with four-fermion interaction

We consider quantum electrodynamics in the quenched approximation including a four-fermion interaction with coupling constantg. The effective potential at stationary points is computed as a function of the coupling constants α andg and an ultraviolet cutoff Λ, showing a minimum of energy in the (α,g) plane for α=α _c =π/3 andg=∞. When we go to the continuum limit (Λ→∞), keeping finite the dynamical mass, the minimum of energy moves to (α=0,g=1), which correspond to a point where the theory is trivial.     

Lattice model calculations for SU(2) Yang-Mills theory in 1 + 1 dimensions

Lattice model techniques are employed to study the low-energy spectrum of SU(2) Yang-Mills theory in 1 + 1 dimensions. The Hamiltonian formulation of Kogut and Susskind is employed. The strong coupling expansion is carried to eighth order for a few of the lower-lying states. These expansions are extrapolated to the continuum limit using Padé approximants, both for finite quark masses and in the non-relativistic limit (quark mass goes to infinity). These methods succeed in giving a qualitative picture of the spectrum, but their quantitative accuracy is poor.