Lattice gauge theory calculations using an improved strong-coupling expansion and matrix Padé approximants

Matrix methods are used to obtain better convergence of low-order lattice calculations. Strong-coupling expansions for the Hamiltonian matrix in a non-degenerate subspace of states are extrapolated to zero lattice spacing using matrix Padé approximants. The method is applied first to the massive Schwinger model and the continuum estimates from different fourth-order calculations compared. Then it is used to calculate the ratios of the π, ? and ω meson masses to the nucleon mass in a Hamiltonian lattice formulation of QCD.     

红外区Dyson-Schwinger方程的两种重整化方案的比较

在胶子和鬼传播子所满足的耦合的Dyson-Schwinger方程中, 采用裸胶子－鬼顶点, 利用两种重整化方案: 解析延拓方法和减除方法, 得到了胶子和鬼传播子的红外行为. 计算表明两种重整化方案在红外区对胶子和鬼传播子得到一致的结果.     

大平板瞬态热传导问题的一种新的近似解法

１引言大平板瞬态热传导问题有着广泛的工程应用背景。对于复杂的初边值条件或含内热源问题,以及工程上常见的多层复合平壁对象,分析求解难度很大甚至无法求解。在此类情况下往往采用数值方法。但是单纯的数值解不便于理解影响该问题的各种参数的物理意义。因此,各种近似分析方法得到了发展［１,２］。但在近似精度上,往往难以对整个时间坐标范围都达到较高的精度,这就使得近似解更多地局限于定性分析。此外,对于不同的初边值条件或含内热源问题,近似解的形式相异,降低了解的通用性。增加了求解的工作量。本文提出一种基于矩阵理论…     

The nature of confined states

We show that in spite of charge confinement in the Schwinger model¹ and its nonconfinement in (QED)₄, the charged states in the two theories have many features in common. A convenient infrared regularization procedure is introduced to facilitate the study of large-distance behaviors in the Schwinger model, particularly those properties that are relevant to the question of when a charged state is physical. One difference that emerges between the two theories is that when a charged state in the Schwinger model is made physical while its energy is kept bounded, the charge goes off to infinity. The end-product could be considered neutral if the charge is defined as the limit of local measurements. On the other hand, if one attempts to change a local charged state in the Schwinger model into a physical state by transporting the localization region to asymptotic distances, the state may end up in either a θ-sector or the corresponding (θ+π)-sector, depending on the direction of transport. A possible generalization of this θ-mixing property to quark-like states in QCD is commented upon.     

Schwinger Formula Revisited

We apply the formal W.K.B. method in the complex plane to the quantum field theory to obtain the Schwinger formula for spin and spinless particles; i.e., we obtain the probability that the vacuum state remains unchanged in presence of a constant electric field. Finally, from Schwinger formula we calculate the probability that n pairs are produced.     

Kinematics of sputtered excited atoms

The kinematics of binary inelastic collisions, when the inelasticity is strong enough in order to influence the collision dynamics, has been derived. It has been shown that neutral and excited sputtered atoms differ from each other in regions of kinetic energy and angular variables. The structure of these physical regions, due to their general character, can be used to obtain direct information on the inelastic processes which are responsible for the formation of the excited states. In particular, on the basis of a limiting angle for the recoiling particle, we show a simple equation and a cross-section which enable us to obtain direct information about inelastic processes. Applications on Si-sputtered species are shown.     

Quark masses from regularized integrals of vector current spectral functions

We give estimates of quark masses from a comparison of two methods of regularizing the coefficient of the Schwinger term. The masses of the first radial excited states of ?, ω, and ? would have to be slightly higher than indicated by the new Orsay data for this method to yield real solutions for the masses of theu, d, ands quarks.     

Field theoretical approach to spin models

We developed a systematic non-perturbative method base on Dyson–Schwinger theory and the Φ-derivable theory for Ising model at broken phase. Based on these methods, we obtain critical temperature and spin spin correlation beyond mean field theory. The spectrum of Green function obtained from our methods become gapless at critical point, so the susceptibility become divergent at Tc. The critical temperature of Ising model obtained from this method is fairly good in comparison with other non-cluster methods. It is straightforward to extend this method to more complicate spin models for example with continue symmetry.     

确定延迟反馈法控制低维混沌系统的控制条件

基于数学上分析延迟系统产生Hopf分支的条件及处理方法,针对用延迟反馈法控制低维混沌系统的情况,提出了确定其控制条件的一般解析方法.利用这种解析方法,可以从理论上得到控制参量间的函数关系.将该方法应用到一些实例中,得到了对实际控制混沌有重要指导意义的理论结果 关键词： 混沌 延迟反馈法 Hopf分支     

Non-perturbative Methods in Relativistic Field Theory

This talk reviews relativistic methods used to compute bound and low energy scattering states in field theory, with emphasis on approaches that John Tjon and I discussed (and argued about) together. I compare the Bethe–Salpeter and Covariant Spectator equations, show some applications, and then report on some of the things we have learned from the beautiful Feynman–Schwinger technique for calculating the exact sum of all ladder and crossed ladder diagrams in field theory.     

The choosing of reproducing kernel particle shape function with mathematic proof

Many mechanical problems can be induced from differential equations with boundary conditions; there exist analytic and numerical methods for solving the differential equations. Usually it is not so easy to obtain analytic solutions. So it is necessary to give numerical solutions. The reproducing kernel particle (RKP) method is based on the Garlerkin Meshless method. According to the Sobolev space and Fourier transform, the RKP shape function is mathematically proved in this paper.     

Quantum Correlation Coefficients for Angular Coherent States

Quantum covariance and correlation coefficients of angular or SU（2） coherent states are directly calculated for all irreducible unitary representations. These results explicitly verify that the angular coherent states minimize the Robertson-Schrodinger uncertainty relation for all spins, which means that they are the so-called intelligent states. The same results can be obtained by the Schwinger representation approach.     

反常、Chern-Simons上链

本文提出一种联络空间上同调的概念,建立这种上同调群与Chern-Simons型示性类系列的同态关系,给出它们在反常、Wess-Zumino有效作用与Schwinger项等问题上的应用;从而概括了Faddeev,宋行长,Zumino等人最近关于这些问题的探讨。 关键词：     

Coherent Schwinger interaction from Darboux transformation

The exactly solvable scalar-tensor potential of the four-component Dirac equation has been obtained by the Darboux transformation method. The constructed potential has been interpreted in terms of nucleon-nuclear and Schwinger interactions of neutral particles with lattice sites during their channeling in the nonmagnetic crystal. The family of exactly solvable interaction Hamiltonians of a Schwinger type is obtained by means of the Darboux transformation chain. The analytic structure of the Lyapunov function of periodic continuation for each of the Hamiltonians of the family is considered.     

AN EXACT SOLUTION OF THE NAIVE SCHWINGER MODEL ON LATTICE

An exact solution of the Naive Schwinger model on lattice is found.The continuous limit of the solution is discussed.The result is that the Naive lattice gauge theory can not cut off the unphysical states of the Schwinger model in the high-energy limit.     

A Note on the Analyticity of Density of States

We consider the d-dimensional Anderson model, and we prove the density of states is locally analytic if the single site potential distribution is locally analytic and the disorder is large. We employ the random walk expansion of resolvents and a simple complex function theory trick. In particular, we discuss the uniform distribution case, and we obtain a sharper result using more precise computations. The method can be also applied to prove the analyticity of the correlation functions.     

Semiclassical calculation of decay rates

Several relevant aspects of quantum-field processes can be well described by semiclassical methods. In particular, the knowledge of non-trivial classical solutions of the field equations, and the thermal and quantum fluctuations around them, provide non-perturbative information about the theory. In this work, we discuss the calculation of the one-loop effective action from the semiclasssical viewpoint. We intend to use this formalism to obtain an accurate expression for the decay rate of non-static metastable states.     

Calculation of the color axial anomaly on the basis of the gauge-invariant spatial point-splitting regularization

The nonsinglet axial anomaly is calculated by employing Schwinger’s point-splitting regularization of the interaction between fermions and a non-Abelian gauge field. This method makes it possible to obtain a covariant expression for the anomaly directly from the effective action for the gauge field. Previously, the anomaly under study was calculated by many other methods. However, all calculations based on the point-splitting regularization (from the pioneering study of Bardeen in 1969) involve a number of intermediate steps and subtractions of specially chosen polynomials in the field.     

Accurate state and parameter estimation in nonlinear systems with sparse observations

Transferring information from observations to models of complex systems may meet impediments when the number of observations at any observation time is not sufficient. This is especially so when chaotic behavior is expressed. We show how to use time-delay embedding, familiar from nonlinear dynamics, to provide the information required to obtain accurate state and parameter estimates. Good estimates of parameters and unobserved states are necessary for good predictions of the future state of a model system. This method may be critical in allowing the understanding of prediction in complex systems as varied as nervous systems and weather prediction where insufficient measurements are typical.     

幂级数展开法计算周期阻尼振子路径积分短时传播子

文章用Schwinger方法与Makri等人发展的幂级数展开法研究了周期阻尼简谐振子的传播子.研究表明,这两种方法所获得的短时传播子非常接近,但是后者比前者要简单得多,这给研究复杂系统的传播子提供了一个简单可靠的方法.