On the Renormalization of Feynman Integrals

An arbitrary Feynman integral is considered for external momenta in the Euclidean region, the usual rotation of energy contours having been used to write the integral as an integral over Euclidean internal momenta. A compactification of the space of internal momenta is defined, and the Feynman integral is written as the integral of a current on this compact manifold. This presentation of the integral is used to give a proof of the convergence criterion for Feynman integrals, and to show that a well-defined renormalized integral may be obtained by a subtraction operation or by analytic renormalization.     

Rubinowicz transform of the MTPO surface integrals

The surface integral of the modified theory of physical optics is reduced to a line integral by using the Rubinowicz transform for the incident scattered fields by an arbitrary aperture in a black surface. The integral theorem of Kirchhoff is applied to the scattering geometry and the diffracted fields are expressed in terms of a line integral along the contour of the diffracting edge.     

First Integrals and Integral Invariants of Relativistic Birkhoffian Systems

For a relativistic Birkhoflan system, the first integrals and the construction of integral invariants are studied. Firstly, the cyclic integrals and the generalized energy integral of the system are found by using the perfect differential method. Secondly, the equations of nonsimultaneous variation of the system are established by using the relation between the simultaneous variation and the nonsimultaneous variation. Thirdly, the relation between the first integral and the integral invariant of the system is studied, and it is proved that, using a t~rst integral, we can construct an integral invarlant of the system. Finally, the relation between the relativistic Birkhoflan dynamics and the relativistic Hamilton;an dynamics is discussed, and the first integrals and the integral invariants of the relativistic Hamiltonian system are obtained. Two examples are given to illustrate the application of the results.     

A solution of radiative transfer in isotropic plane-parallel atmosphere by integrating Milne equation

In this paper we solve the inversion problem of the radiative transfer process in the isotropic plane-parallel atmosphere by iterative integrations of the Milne integral equation. As a result, we obtain the scattering function in the form of a cubic polynomial in optical thickness. The author has already solved the same problem by iterative integrations of Chandrasekhar's integral equation. In the Milne integral equation, both the cosines of the viewing angles and the optical thickness are integral variables, while in Chandrasekhar's integral equation the cosines of the viewing angles are variables but the optical thickness is not. We derive several series of exponential-like functions as intermediate derivations. Their convergences are evaluated by the author's previous work in the solution of Chandrasekhar's integral equation. The truncated scattering function up to the third order in optical thickness thus obtained is identical to that obtained from Chandrasekhar's integral equation, though their apparent forms are different. Chandrasekhar pointed out that the solution of Chandrasekhar's integral equation does not have a uniqueness of solution. The Milne equation, in contrast, has been proven to have a unique solution. We discuss the uniqueness of the solution by these two methods.     

A New Solution to the Hirota-Satsuma Coupled KdV Equations by the Dressing Method

The Hirota-Satsuma coupled KdV equations associated 2×2 matrix spectral problem is discussed by the dressing method, which is based on the factorization of integral operator on a line into a product of two Volterra integral operators. A new solution is obtained by choosing special kernel of integral operator.     

动力边界元法中的强奇异积分问题

本文讨论了动力边界元法中的奇异积分问题,对其中的强奇异积分提出了一个有效的计算方法.该方法从合非零初始态的边界积分方程出发,利用动力方程的特解间接地确定了主系数(即所谓强奇异积分),从而避免了直接计算强奇异积分的困难.根据该方法编制了计算程序,并给出了一个简单算例。     

New framework for the Feynman path integral

The well-known Fourier integral solution of the free diffusion equation in an arbitrary Euclidean space is reduced to Feynmannian integrals using the method partly contained in the formulation of the Fresnelian integral. By replacing the standard Hilbert space underlying the present mathematical formulation of the Feynman path integral by a new Hilbert space, the space of classical paths on the tangent bundle to the Euclidean space (and more general to an arbitrary Riemannian manifold) equipped with a natural inner product, we show that our Feynmannian integral is in better agreement with the qualitative features of the original Feynman path integral than the previous formulations of the integral.     

高功率光纤啁啾脉冲放大光源中的B积分受限

基于金斯堡-朗道方程模型,针对100kHz光纤啁啾脉冲放大系统中的B积分受限问题进行了理论分析,包含群速色散、增益色散、平均功率饱和和能量饱和效应及自相位调制效应。给出了典型放大器构型下脉冲可压缩性随B积分的变化关系。得到了展宽脉冲宽度为1ns条件下,亚ps压缩脉冲对系统总的B积分限值约为40rad。对短间隔脉冲串放大特性和B积分进行了理论研究,验证了在单脉冲B积分受限不变的情况下可以实现总脉冲能量倍增。     

超短脉冲在光学介质中传输的B积分特性

从非线性薛定谔方程出发,利用分步傅里叶算法对其进行求解,数值模拟了在超短脉冲激光系统中几种光学介质中的B积分传输规律,并对其特性进行了简要分析。数值计算结果表明,初始脉冲的输入光强与光学介质的增益系数的增大会使B积分值增加。脉冲形状对B积分值有一定影响,与飞秒高斯脉冲比较,当输入为ps级的啁啾脉冲时,B积分较小。针对所选计算模型,适当的群速色散与高阶色散可以减小B积分值。这对超短脉冲放大系统的设计有参考意义。     

导体表面电荷不均匀分布的数值计算

用积分法分析了被屏蔽导体表面的电荷分布,提出了一种具有特殊场域的求解电场 方法,为了求解在奇异点的积分,提出了一系列解析公式,可以避免复杂的数学处理,还分析了一个具体实例的临近效应,讨论了积分法的计算精度 。     

自旋为任意整数的传播子

以自旋为任意整数的自由粒子的波函数(Bargmann-Wigner方程的解)为基础，进一步研究了 自旋为任意整数的投影算符和传播子.证明了Behrends和Fronsdal所构造的投影算符是正确 的.导出了自旋为任意整数的场的一般对易规则和费恩曼传播子的一般表达式. 关键词： 整数自旋 投影算符 对易规则 费恩曼传播子     

高功率光纤啁啾脉冲放大光源中的B积分受限

基于金斯堡-朗道方程模型,针对100 kHz光纤啁啾脉冲放大系统中的B积分受限问题进行了理论分析,包含群速色散、增益色散、平均功率饱和和能量饱和效应及自相位调制效应。给出了典型放大器构型下脉冲可压缩性随B积分的变化关系。得到了展宽脉冲宽度为1 ns条件下,亚ps压缩脉冲对系统总的B积分限值约为40 rad。对短间隔脉冲串放大特性和B积分进行了理论研究,验证了在单脉冲B积分受限不变的情况下可以实现总脉冲能量倍增。     

基于积分图像的人体肢体检测算法

 为了实现视频序列图像中运动人体肢体的检测,提出了一种基于积分图像和类哈尔特征的检测方法,类哈尔特征(Haar like feature)因其固有的特点,适用于检测矩形或类矩形的图像区域,积分图像的特点是可以利用类哈尔特征快速定位人体肢体在图像中的位置。积分图像用于表示视频中的原始图像,边缘检测模板与原始视频每一帧进行卷积之后,通过累加计算可以得到该图像的积分图像,然后利用类哈尔算子,根据设定的阈值,即可以准确定位人体肢体位置。实验结果表明：该方法较背景减除法检测人体肢体准确。     

First Integrals and Integral Invariants of Relativistic Birkhoffian Systems

For a relativistic Birkhoffian system, the first integrals and the construction of integral invariants arestudied. Firstly, the cyclic integrals and the generalized energy integral of the system are found by using the perfectdifferential method. Secondly, the equations of nonsimultaneous variation of the system are established by using therelation between the simultaneous variation and the nonsimultaneous variation. Thirdly, the relation between the firstintegral and the integral invariant of the system is studied, and it is proved that, using a first integral, we can construct anintegral invariant of the system. Finally, the relation between the relativistic Birkhoffian dynamics and the relativisticHamiltonian dynamics is discussed, and the first integrals and the integral invariants of the relativistic Hamiltoniansystem are obtained. Two examples are given to illustrate the application of the results.     

Path integration in conical space

Quantum mechanics in conical space is studied by the path integral method. It is shown that the curvature effect gives rise to an effective potential in the radial path integral. It is further shown that the radial path integral in conical space can be reduced to a form identical with that in flat space when the discrete angular momentum of each partial wave is replaced by a specific non-integral angular momentum. The effective potential is found proportional to the squared mean curvature of the conical surface embedded in Euclidean space. The path integral calculation is compatible with the Schrödinger equation modified with the Gaussian and the mean curvature.     

Quantum Cosmology with Hyperbolic Potential

For an FRW model with a minimally coupled scalar field having hyperbolic(exponential) potential we evaluate the wave function both by solving theWheeler-Dewitt (WD) equation and by evaluating the path integral. The WDequation is solved in configuration as well as in momentum space, while thepath integral is evaluated by dividing the lapse integral into a number of pieces.     

Instability of Solution of Phase Retrieval in Direct Diffraction Phase-Contrast Imaging with Partially Coherent X-Ray Source

The theoretical model of direct diffraction phase-contrast imaging with partially coherent x-ray source is expressed by an operator of multiple integral. It is presented that the integral operator is linear. The problem of its phase retrieval is described by solving an operator equation of multiple integral. It is demonstrated that the solution of the phase retrieval is unstable. The numerical simulation is performed and the result validates that the solution of the phase retrieval is unstable.     

菲涅耳-基尔霍夫积分与半波带法分析衍射光谱

惠更斯菲 涅耳原理指出光的衍射本质是无穷多次波的相干叠加.在研究衍射光谱的强度时可使用菲涅耳-基尔霍夫衍射积分进行计算,但该积分的计算较为复杂.为了简化计算而引入菲涅耳半波带的概念,把积分运算简化为振幅矢量的叠加,从而在研究衍射时由菲涅耳-基尔霍夫衍射积分过渡到菲涅耳半波带法.在菲涅耳半波带法中波前上相邻两个半波带到达叠加点的光程差为半个波长,从而导致相位差π.因此相邻两个半波带引起的振动在叠加点发生相消,最终叠加点的光强由发出次波的半波带数目的奇偶性决定.奇数个半波带在叠加点的光强得到加强,偶数个半波带在叠加点的光强发生相消.     

Contour integration on super-Riemann surfaces

Super contours are defined to be superconformal maps of real (1,1)-dimensional superspace into complex (1,1)-dimensional superspace. A method for integration along supercontours is defined in terms of a modified Berezin integral on (1,1)-dimensional real superspace. The natural transformation properties of this modified Berezin integral are inherited by the contour integral, so that the contour integral of a half form on a general super-Riemann surface is defined.     

Quantum adiabatic approximation to interacting boson-fermion systems

We present an adiabatic approximation method for the path integral of the Fermi field in the presence of a Bose field. The adiabatic phenomenon recently found by Berry and Simon is used for evaluating the Grassman path integral. Then we obtain the path integral of the effective action analogous to a magnetic field, and the quantization rule is derived by applying the semiclassical quantization method.