QUANTUM CHROMODYNAMICS

<正>Revised October 2013 by S.Bethke(Max-Planck-Institute of Physics,Munich),G.Dissertori(ETH Zurich),and G.P.Salam(CERN and LPTHE,Paris).9.1.Basics Quantum Chromodynamics(QCD),the gauge field theory that describes the strong interactions of colored quarks and gluons,is the SU(3)component of the SU(3)xSU(2)xU(l)Standard Model of Particle Physics.The Lagrangian of QCD is given by     

LATTICE QUANTUM CHROMODYNAMICS

<正>Updated September 2013 by S.Hashimoto(KEK),J.Laiho(Syracuse University),and S.R.Sharpe(University of Washington).18.1.Lattice regularization of QCD Gauge theories form the building blocks of the Standard Model.While the SU(2)and U(l)parts have weak couplings and can be studied accurately with perturbative methods,the SU(3)component—QCD—is only amenable to a perturbative treatment at high energies.The growth of the coupling constant in the infrared—the flip-side of asymptotic freedom—requires the use of non-perturbative methods to determine the low energy properties of QCD.Lattice gauge theory,proposed by K.Wilson in 1974[1],provides such a method,for it gives a non-perturbative definition of vector-like gauge field theories like QCD.In lattice regularized QCD—commonly called lattice QCD or LQCD—Euclidean space-time is discretized,usually on a hypercubic     

PARISI-SOURLAS CONFINEMENT MECHANISM OF QUANTUM CHROMODYNAMICS

Using Parisi and Sourlas dimensional reduction, four-dimensional quantum chromodynamics is reduced to a two-dimensional principal chiral model by suitable superspace embedding. The frame T^a cannot be regarded as a fixed one and the frame connection field \varω_μ(x) becomes a dynamical gauge field in two dimensions, giving rise to a confining potential. As a result of the original SU(3) Yang-Mills field obtains another SU(3) local symmetry and turns into SU(3)×SU(3) local symmetry－one group element as exp (iδ\varphi^aT^a) with fixed frame T^a, the other gauging the frame T^a.     

SYNTHESIS OF PERTURBATIVE AND NONPERTURBATIVE QUANTUM CHROMODYNAMICS

Hadronic structure in QCD has been analyzed by using the Fock state wavefunctions of hadrons defined by quantizing quantum chromodynaraics at equal time of the light-cone. They provide a unified approach to QCD phenomenology. We have presented a convenient method for operator product expansion in the external background fields and have obtained the distributior: amplitude moments values from QCD sum rule by introdution the condensate effect of quarks and gluons. These results are in agreement with the present data.     

QUANTUM CHROMODYNAMICS AS THE TRORY OF INTERACTIONS

Recent developmeht of testing QCD as the theory of strong interactions is reviewed. Emphasis is put on the success of perturbative QCD and the determination of the fundamental scale parameter scale parameter A. Recent development of heavy quarkonium physics is also reviewed from the point of view of QCD and the possibility that future heavy quarkonium experiments can provide further quantitative QCD tests is discussed.     

THE U(90) DYNAMICAL SYMMETRY IN LIGHT NUCLEI

In the IBM4,when s.d.g bosons are presented,the symmetry group of the system is U(90) In this paper,the group chain.U₉₀ U₁₅(sdg)×U₆(ST) SU₁₅(sdg)×U₆(ST) SU₅(sdg)× O₆(ST) SO₅(dg)×O₃(S)×O₃(T) O₃(dg)×O₃(S)×O₃(T) O₃(J)×O₃(T) is discussed,the reduction rules and the typical energy spectra are obtained.An example of a spectrum with this dynamical symmetry is found out,where the even-even nucleus ³⁴S and odd-odd nucleus ³⁴Cl are in one multiplet.     

THE INFRARED STRUCTURE AND THE ELECTROMAGNETIC FORM FACTORS OF QUANTUM CHROMODYNAMICS IN TWO DIMENSIONS

We discuss a model of quantum chromodynamics in 1+1 dimension.Using't Hooft's 1/N expansion and considering the effects of the infrared structure in non-Abelian gauge theories by assuming that the coupling g²（t）～1/t^κ-1,the Straton's Pro-pagator and the Bethe-Salpeter equation of mesons are obtained;the propertiesof the meson wave functions and their characteristics are also discussed.From thebehaviour of the electromagnetic form factors and the deep inelastic scattering struc-ture functions obtained,it follows that κ≤2.     

WEAK COUPLING APPROXIMATE SCHWINGER-DYSON EQUATION OF THE STRATON'S PROPAGATOR IN QUANTUM CHROMODYNAMICS AND ITS SOLUTIONS

The weak coupling approximate Schwinger-Dyson equation of the straton's pro-pagator in 4-dimensional QCD theory and the problem of the straton's confinement are discussed. It is proved that, when we choose Landaugauge, the obtained Sch-winger-Dyson integral equation of the straton's propagator can be transformed into a very simple form. Then we change it into a first order non-linear differential equation. It has two solutions: a confining solution and a solution that has no con-finement for the stratons. The effective potential in QCD is derived by functional method, and the ground-state energy difference between these two solutions is discussed. In our approximation, we calculate the vacuum graph to the 2-loop diagrams, We may conclude that stratons are not confined in our approximation.     

动力学对称群方法对三原子分子高激发振动态的理论研究

利用动力学对称群方法研究了弯曲三原子分子的振动高激发态能谱-该方法显示：三原子分子的动力学对称性为U₁(4)U₂(4),则三原子分子的Hamiltonian量可写成代数的各元素之和,通过李代数处理而求得分子代数Hamiltonian量的本征值,进而得到分子的振动能谱-并具体计算了O₃分子- 关键词：     

AN IMPROVED EFFECTIVE POTENTIAL APPROACH TO DYNAMICAL SYMMETRY BREAKING

We have developed, in this paper, a method for evaluating effective potential for local composite fields based on loop expansion by first renormalizing the generating functional of connected Green's functions and then making the Leqendre transformation. A consistency condition reflecting the fact that no condensate effect occurs at tree level is proposed, which plays an important role in this method. The method is illustrated through the Gross-Neveu model. This method can be applied to a wider class of models than can the auxiliary field method.     

二能级系统中光场压缩与原子偶极压缩间的对称特性

揭示了共振Ｊａｙｎｅｓ-Ｃｕｍｍｉｎｇｓ模型中光场压缩与原子偶极压缩间的对称特性，并探讨了各种非线性作用包括非共振作用，虚光子过程，任意强度耦合及类Ｋｅｒ介质与腔作用对光场压缩与原子偶极压缩间的对称特性的影响，还讨论了（２ｍ＋１）量子共振下两种压缩间的内在关系     

DYNAMICAL SYMMETRY BREAKING IN MODELS OF SPIMOR FIELDS WITH QUARTIC INTERACTIONS IN (1+1) DIMENSIONS

A nonperturbative method, namely, variarional method together with canonical transformations, is developtd to study dyndcal symmetry breaking. This method has been applied in the models of two dimensional massless fermion fields with quartic interactions. The results imply that the mechanism of dynamical symmetry breaking bears some analogy to the phenomenon of superconductivity. The new vacuum |õ> is just a relativistic BCS groundstate, In this vacuum |õ>, we can observe a quasi-particle with mass "MP" Furthermore, correlative vacuum |õ> exists and the mesons emerge with masses "O" and "2M_F". It is also shown that dynamical symmetry breaking always occurs in the models with infrared slavery and asymptotic freedom, while it is meaningless to dis-cuss dynamical symmetry breaking in infrared stable theory.     

三维量子自旋玻璃理论(Ⅲ)──replica对称破缺解

利用推广的Ｐａｒｉｓｉ量子ｒｅｐｌｉｃａ对称破缺方案，将我们以前提出的理论推广到ｒｅｐｌｉｃａ对称破缺，获得一组新的自旋自作用和自旋玻璃序参数的自洽方程，导出局域磁化率．通过计算ｒｅｐｌｉｃａ对称破缺自由能，发现矢量自旋玻璃模型的ｍｐｌｉｃａ对称解存在着低温破缺． 关键词：     

ON THE DYNAMICAL SYMMETRY BREAKING FOR THE N=l PURE SUPERSYMMETRIC YANG-MILLS MODEL

An approximate effective Lagrangian of composite operators in superfield formalism for the N=l pure supersymmetric Yang-Mills model is obtained with the help of renormalization group equations for the generating functional. While the supersymmetry is always kept unbroken by this effective Lagrangian we find that the chiral symmetry may and may not be unbroken.     

THE SYMMETRY OF STRATONS IN

In this paper,the color symmetry of stratons for a theoretical model proposed some times ago is investigated.This symmetry contains two kinds of transformations, the first is color gauge transformations which leave the color mumber of stratons conserved,the second is color permutations which indicate the equivaluence of dif- ferent color stratons.The structure of this symmetry group（S3α）is investigated.The irreducible representations（IR's）of S3α and the reduction of their direct product are given.The relation between IR's of S3α and those of color U（3）group is discussed. In a simplest physical model only two neutral vector gluons are needed and the super-strong ihteraetions among stratons exhibit saturation properties similar to but somewhat different from the case of the Han-Nambu model.Not only the color singlet, but also other color neutral states belonging to IR's 2 or 1 of S3α all belong to the lowest energy level of the super-strong interactions.If there were eight degenerate vector gluons belonging to IR's 2 and 6,the Han-Nambu model would be reproduced.     

三维量子自旋玻璃理论(Ⅰ)——稳态Replica对称近似

利用虚时泛函积分技术和Replica方法,建立了具有Dazyaloshinskii-Moriya各向导性和铁磁相互作用的三维量子自旋玻璃理论。在稳态Replica对称近似下,确定了自旋自相互作用、自旋玻璃序参量和磁化强度的自洽方程组,获得了对角磁化率与序参数间的关系,给出了与序参数有关的自由能密度,克服了有关理论的低温失效。 关键词：     

利用比特配对来保持量子计算中的相干性

提出了一种简单高效的方案，用以克服量子计算中的消相干，该方案本质性地利用了消相干过程中的合作效应及相干保持态．文章阐明了该方案的主要思想．     

量子信息讲座续讲 第一讲 量子计算中的因子分解

因子分解对所有的现行计算机而言是难解的 .这是现在通用的公共加密系统的基础 .文章介绍了在量子计算机上进行的Shor量子算法 ,即利用量子态的相干叠加和纠缠特性以及量子逻辑门实现量子计算的方法 ;并着重从理论原理和实验实现这两方面说明利用余因子函数和离散傅里叶变换使这种量子算法对因子分解是有效的 .