高温下夸克场真空图中的红外发散

用热传播子的实时形式对高温条件下夸克(忽略质量)场三圈真空图进行了详细地计算,找出了其中和费米–狄拉克统计因子有关的红外发散积分的类型,并对这种发散积分进行了正规化,进一步把真空图中的红外发散全部孤立出来了.     

有限温度下无质量场真空图中红外发散的正规化

讨论无质量δ³理论标量场和胶子场三圈真空图中的红外发散和它的正规化,给出了它在D维空间的解析延拓表达式,并讨论了如何分离出交缠发散时的红外发散和共线发散.     

有限温度下无质量φ3理论中角度红外发散的正规化

讨论了无质量标量场3理论三圈真空图中的角度红外发散以及它的维数正规化方案,并给出了它在D维空间的解析表达式.     

有限温度下无质量ψ^3理论中角度红外发散的正规化

讨论了无质量标量场ψ＾３理论三圈真空图中的角度红外发散以及它的维数正规化方案，并给出了它在Ｄ维空间的解析表达式。     

有限温度下胶子场三圈真空图中的红外发散

用热传播子的实时形式对有限温度下胶子场的三圈真空图进行了详细的计算，在维数正规化方案下把真空图中的红外发散全部孤立出来了.     

任意规范下有限温度二圈QED热力学势及其交叉发散

采用有限温度下维数正规化的方法在任意协变规范下精确地计算了双圈ＱＥＤ的热力学势及其交叉发散．计算表明交叉发散彼此相消且所得的结果与规范的选取无关．     

一般情形下的碰撞积分修正

众所周知,将玻耳兹曼积分应用于等离子体,由于忽略了集体效应,导致积分对数发散。另外,Balescu-Lenard碰撞理论考虑了集体效应,克服了k→0对数发散困难,但又有k→0积分发散。对于等离子体参量g=1/nλD~3《1情形,文[4]已得出克服k→0积分发散的方法。但对g≥1情形,k→0积分发散问题仍未解决。本文改进了粒子分布函数展开求得包括g<1及g≥1在内的一般情形即南k→0与k→0均收敛的碰撞积分。     

圈图函数中的红外发散

介绍一种判断和计算圈图函数红外发散的有效方法.利用该方法研究了C函数(即三点圈图函数)和D函数(即四点圈图函数)的红外发散性质,并且给出常见的C函数的红外发散形式.     

有限温度QED中的轫致辐射修正

用有限温度场论方法,通过计算费曼图分析了在QED中由于温度效应导致的新红外发散.结果表明零温场论中的红外发散和由温度效应引起的红外发散可以用描写虚过程的费曼图同时消除.计算了轫致辐射中光子的辐射几率,在Eikonal近似下所得到的结果和半经典近似给出的结果一致.     

发散光束小尺度自聚焦特性的研究

研究了发散光束的小尺度自聚焦效应。从非线性傍轴波动方程出发,利用坐标变换,推导出发散光束小尺度扰动的传输方程,进而得到小尺度扰动增长的临界频率、最大增长频率和相应B积分值的变化规律。研究了发散光束初始曲率半径对小尺度自聚焦效应的影响。结果表明,对于一定的传输距离,随着发散光束初始曲率半径的减小,小尺度扰动的最大增长频率减小,相应的最大增益减小,即B积分值也减小。对于一定的初始曲率半径,随着传输距离的增大,B积分值增长变缓,并最终停止。利用局部能量守恒定律研究了发散光束的成丝距离,发现小的初始曲率半径可以延长成丝距离。     

Infrared Divergences of Three-Loop Vacuum Graghs of Gluon Field at Finite Temperature

The kinds of infrared divergent integrals in three-loop vacuum graghs of gluon field at finite temperature are pointed out and their regularization is discussed. All of the infrared divergences in three-loop vacuum graghs of gluon field are isolated.     

Scalar one-loop four-point integral with one massless vertex in loop regularization

The scalar one-loop four-point function with one massless vertex is evaluated analytically by employing the loop regularization method. According to the method, a characteristic scale μ_s is introduced to regularize the divergent integrals. The infrared divergent parts, which take the form of ln~2(λ~2/μ_s~2)and ln(λ~2/μ_s~2)as μ_s→ 0 where λ is a constant and expressed in terms of masses and Mandelstam variables, and the infrared stable parts are well separated. The result is shown explicitly via 44 dilogarithms in the kinematic sector in which our evaluation is valid.     

A systematization for one-loop 4D Feynman integrals

We present a strategy for the systematization of manipulations and calculations involving divergent (or not) Feynman integrals, typical of the one-loop perturbative solutions of QFT, where the use of an explicit regularization is avoided. Two types of systematization are adopted. The divergent parts are put in terms of a small number of standard objects, and a set of structure functions for the finite parts is also defined. Some important properties of the finite structures, specially useful in the verification of relations among Green's functions, are identified. We show that, in fundamental (renormalizable) theories, all the finite parts of two-, three- and four-point functions can be written in terms of only three basic functions while the divergent parts require (only) five objects. The final results obtained within the proposed strategy can be easily converted into those corresponding to any specific regularization technique providing an unified point of view for the treatment of divergent Feynman integrals. Examples of physical amplitudes evaluation and their corresponding symmetry relations verification are presented as well as generalizations of our results for the treatment of Green's functions having an arbitrary number of points are considered.     

Dimensional regularization of infrared divergences

An analysis of the application of dimensional regularization to infrared divergences in lowest order radiative corrections is presented. The main emphasis of the paper is to show explicitly how dimensional regularization can lead in some cases of considerable interest to very simple and elegant evaluations of infrared divergent contributions and their associated finite parts, and to pinpoint the mathematical reason for the equivalence with the traditional method of regularization.     

Gravitational divergences of the electromagnetic interactions of massive vector particles

In a search for the explanation of the finite quantum gravity corrections to anomalous moments we examined a spontaneous broken O(3) model with Yang-Mills particles and Higgs scalars coupled to gravitons. We found several new cancellations which prove that the coupling of all these particles together does not produce new counterterms apart from these which are known to exist in the subsystems and the cosmological term. The finiteness of the anomalous magnetic moment of a massive spin-1 particle is necessary for this to be valid. The finiteness of the anomalous quadrupole moment is a consequence of a known cancellation in the Einstein-Yang-Mills system. We also checked infrared finiteness and showed how to treat logarithmically divergent massless integrals in dimensional regularization.     

Note on Higgs Decay into Two Photons H → γγ

The Higgs decay H →γγ due to the virtual W-loop effect is revisited in the unitary gauge by using the symmetry-preserving and divergent-behavior-preserving loop regularization method,which is realized in the fourdimensional space-time without changing original theory.Though the one-loop amplitude of H →γγ is finite as the Higgs boson in the standard model has no direct interaction with the massless photons at tree level,it involves both tensor-type and scalar-type divergent integrals which can in general destroy the gauge invariance without imposing a proper regularization scheme to make them well-defined.As the loop regularization scheme can ensure the consistency conditions between the regularized tensor-type and scalar-type divergent irreducible loop integrals to preserve gauge invariance,we explicitly show the absence of decoupling in the limit M W /M H → 0 and obtain a result agreeing exactly with the earlier one in the literature.We then clarify the discrepancy of the earlier result from the recent one obtained by R.Gastmans,S.L.Wu and T.T.Wu.The advantage of calculation in the unitary gauge becomes manifest in that the non-decoupling arises from the longitudinal contribution of the W gauge boson.     

Summation of divergent series and Zeldovich’s regularization method

A method for summing divergent series, including perturbation-theory series, is considered. This method is an analog of Zeldovich’s regularization method in the theory of quasistationary states. It is shown that the method in question is more powerful than the well-known Abel and Borel methods, but that it is compatible with them (that is, it leads to the same value for the sum of a series). The constraints on the parameter domain that arise upon the removal of the regularization of divergent integrals by this method are discussed. The dynamical Stark shifts and widths of loosely bound s states in the field of a circularly polarized electromagnetic wave are calculated at various values of the Keldysh adiabaticity parameter and the multiquantum parameter.