重整化群变换应用于U(1)规范理论的定量分析

在Migdal及Migdal-Kadanoff重整化群变换方案中,我们导出了U(1)格点规范理论的强耦合(高温)近似和弱耦合(低温)近似,同时还得到了包括中间耦合区的数值结果。上述结果与严格的强耦合展开、弱耦合展开以及Monte-Carlo模拟结果进行了比较。 关键词：     

含时空关联噪声的非局域及各向异性Kardar-Parisi -Zhang方程的直接标度分析

将直接标度分析方法推广应用到含时间空间关联噪声的非局域及各向异性KardarParisiZhang方程的动力学标度分析中,分别得到了方程在强耦合区和弱耦合区的标度指数值.在弱耦合区得到的标度指数能与使用动力学重整化方法得到的结果相吻合 关键词： 表面生长 标度分析 KPZ方程     

非局域Lai-Das Sarma-Villain方程动力学标度性质的研究

使用动力学重整化群和直接标度分析的方法研究了非局域Lai-Das Sarma-Villain方程的动力学标度性质.动力学重整化群分析表明非局域非线性项的存在能够导致新的固定点和连续变化的动力学标度指数的产生.使用直接标度分析方法则分别得到了在弱耦合和强耦合区内的标度指数值.在弱耦合区域内得到的标度指数与动力学重整化方法得到的标度指数值能很好地吻合. 关键词： 表面生长 动力学重整化群分析 标度分析     

直接标度分析动力生长

用直接标度分析方法研究了分子束外延生长和在长程时间、空间关联条件下的动力生长过程。分别得到了在强、弱耦合区的粗糙指数和动力学指数,并对其结果进行了讨论,说明了其弱耦合的结果与动力重整化群的结果一致的原因。 关键词：     

格点规范理论中|△S|=2的弱作用矩阵元

本文用格点规范理论的强耦合展开方法,计算|△S|=2的弱作用矩阵元.由此得到的K_L-K_S质量差是和介子质量谱的强耦合展开计算结果相容的,并且与实验结果接近.     

热标量场等离子体激元阻尼率的临界行为

在闭合时间路径的实时温度场论的框架下,导出了热重整化群方程.热重整化群方程的数值解表明热标量场的耦合常数随温度跑动.将热重整化群方程应用到对称性自发破缺的φ4理论,我们考察了具有有限动量的等离子体激元阻尼率在自发破缺对称性恢复的相变温度下的临界行为.当温度趋于临界温度时,结果表明耦合常数随温度的跑动导致有限动量的等离子体激元阻尼率逐渐减小到零,与不考虑耦合常数随温度的跑动得到的趋势相反.解决了把耦合常数看成常量导致的与临界趋缓规律的矛盾.     

含有广义守恒律的生长方程标度奇异性的直接标度分析

利用直接标度分析方法研究一个含有广义守恒律生长方程的标度奇异性,得到强弱耦合区域的奇异标度指数.作为其特殊情况,这个方程包含Kardar-Parisi-Zhang（KPZ）方程、 Sun-Guo-Grant（SGG）方程以及分子束外延（MBE）生长方程,并能对其进行统一的研究.研究发现, KPZ方程和SGG方程,无论在弱耦合还是在强耦合区域内都遵从自仿射Family -Vicsek正常标度规律;而MBE 方程在弱耦合区域内服从正常标度,在强耦合区域内能呈现内禀奇异标度行为.这里所得到生长方程的奇异标度性质与利用重正化群理论、数值模拟以及实验相符很好. 关键词： 标度奇异性 强耦合 弱耦合     

格点规范理论中│ΔS│=2的弱作用矩阵元

本文用格点规范理论的强耦合展开方法,计算│ΔS│=2的弱作用矩阵元.由此得到的K_L-K_S质量差是和介子质量的强耦合展开计算结果相容的,并且与实验结果接近.     

用重整化群流方程方法求解t-J模型元激发能谱

t-J模型是研究电子强关联作用和高T_c超导理论的重要模型之一.将重整化群方法应用于t-J模型，得出相应的流方程，再由流方程求解t-J模型的元激发能谱，并利用函数的对称性，解出t-J模型在零温条件下能谱的具体表达式，最后与常规的格林函数方法所得的结果作了比较. 关键词： 重整化群 t-J模型 流方程     

阿贝尔手征群陪集纯规范场的恒等式和重整化

导出了与"阿贝尔手征群陪集空间纯规范场的生成泛函路径积分测度和有效作用量联合起来在手征群变换下具有不变性"相应的恒等式.利用此恒等式建造了重整化方程,并由方程的解将阿贝尔手征群陪集纯规范场理论重整化.     

The finite temperature renormalization group equation in λφ4 theory

The renormalization group equation at finite temperature is studied in the context of λφ⁴ theory. Three methods of deriving the finite temperature renormalization group equations are presented. The result shows that the effective mass becomes large as the temperature increases while the effective coupling constant becomes small.     

Limit cycles in quantum theories

Renormalization group limit cycles and more chaotic behavior may be commonplace for quantum Hamiltonians requiring renormalization, in contrast to experience based on classical models with critical behavior, where fixed points are far more common. We discuss the simplest quantum model Hamiltonian identified so far that exhibits a renormalization group with both limit cycle and chaotic behavior. The model is a discrete Hermitian matrix with two coupling constants, both governed by a nonperturbative renormalization group equation that involves changes in only one of these couplings and is soluble analytically.     

One-loop-dimensional reduction of the linear σ model

We perform the dimensional reduction of the linear σ model at one-loop level. The effective potential of the reduced theory obtained from the integration over the nonzero Matsubara frequencies is exhibited. Thermal mass and coupling constant renormalization constants are given, as well as the thermal renormalization group equation which controls the dependence of the counterterms on the temperature. We also recover, for the reduced theory, the vacuum unstability of the model for large N.     

Thermal QCD

By the methbd of the gauge field theory at finite temperature, the static thermodynamic properties in quark-gluon plasma are studied in detail. According to the renormalization group equation, an analytic expression of the running coupling constant g(T, p) with the temperature T is obtained.     

Functional renormalization group at large N for disordered systems

We introduce a method, based on an exact calculation of the effective action at large N, to bridge the gap between mean-field theory and renormalization in complex systems. We apply it to a d-dimensional manifold in a random potential for large embedding space dimension N. This yields a functional renormalization group equation valid for any d, which contains both the O(epsilon=4-d) results of Balents-Fisher and some of the nontrivial results of the Mezard-Parisi solution, thus shedding light on both. Corrections are computed at order O(1/N). Applications to the Kardar-Parisi-Zhang growth model, random field, and mode coupling in glasses are mentioned.     

提高重整化群精度的一个尝试

以热逾渗分析散粒体导热率时,利用重整化群方法改变粗视化程度来定量地获得导热率的变化。实践表明这只有设法提高重整化群的精度才会有较好的结果。本文以逾渗转变为例,针对b=2的相关尺度变化方式,分别对二维和三维实空间的重整化变换进行了修正,导出了相应的重整化方程。计算精度有明显提高,计算结果与实验值更接近。     

Coupling Constant in High Temperature QCD and Deconfinement Phase Transition

Finite temperature renormalization group equation is employed to investigate the effective coupling constant of QCD with respect to temperature.At high temperature,it is very small over the entire region of momentum,this leads to the property of deconfinement of QCD.     

Multi-jet event rates in deep inelastic scattering and determination of the strong coupling constant

Jet event rates in deep inelastic ep scattering at HERA are investigated applying the modified JADE jet algorithm. The data are corrected for detector and hadronization effects and then compared with perturbative QCD predictions using next-to-leading order calculations. The strong coupling constant is determined evaluating the jet event rates. Values of are extracted in four different bins of the negative squared momentum transfer in the range from 40 GeV to 4000 GeV. A combined fit of the renormalization group equation to these several values results in     

Non-perturbative QEG corrections to the Yang–Mills beta function

We discuss the non-perturbative renormalization group evolution of the gauge coupling constant by using a truncated form of the functional flow equation for the effective average action of the Yang–Mills-gravity system. Our result is consistent with the conjecture that quantum Einstein gravity (QEG) is asymptotically safe and has a vanishing gauge coupling constant at the non-trivial fixed point.     

QCD One-Loop Effective Coupling Constant and Quark Mass Given in a Mass-Dependent Renormalization

The QCD one-loop renormalization is restudied in a mass-dependent subtraction scheme in which the quark mass is not set to vanish and the renormalization point is chosen to be an arbitrary time-like momentum. The correctness of the subtraction is ensured by the Ward identities which are respected in all the processes of subtraction.By considering the mass effect, the effective coupling constant and the effective quark masses derived by solving the renormalization group equations are given in improved expressions which are different from the previous results.