The Feynman path-integral variational theory is the best way to compute the ground-state energy of bound polarons.
费曼路径积分的变分方法是计算束缚极化子基态能的最有效方法。
OK, so, we've seen that if we have a vector field defined in a simply connected region, and its curl is zero, then it's a gradient field, and the line integral is path independent.
一个向量场,如果定义在单连通区域并且旋度为零，那么它就是一个梯度场，并且其上的线积分与路径无关。
I mean if that is your favorite path then that is fine, but it is not very easy to compute the line integral along this, especially since I didn't tell you what the definition is.
如果你喜欢也可以，但是沿着这条路径积分却不好计算，尤其是还没告诉你曲线的定义。
Or, if you really don't like that line integral, you could close the path by adding some other line integral to it, and then compute using Green's theorem.
如果不喜欢计算线积分，可以通过增加一条线积分让曲线封闭起来，然后就可以用格林公式来计算了。
We say that the line integral is path independent.
我们称之为线积分与积分路径无关。
The path integral quantization is applied to modem physics more and more extensively.
路径积分量子化在近代物理中的应用愈来愈广泛。
Feynman's path integral is used to analyze quantitatively the Fraunhofer circle aperture diffraction. The quantum eigenstate of circle aperture diffraction is elaborated.
利用费曼路径积分理论，对夫琅和费圆孔衍射的光子衍射态进行定量分析，阐明圆孔衍射的量子本征。
The expression of quantum correction of the multidimensional fission rate at finite temperature is obtained by a path integral method.
用路径积分方法得到了有限温度下多维量子裂变速率的表达式。
Finally, the calculations are made on a concrete example to illustrate the application of the path integral in discrete bases to Physics.
最后，就分立基路径积分在物理学中的应用，结合具体实例作了计算和处理。
The path integral Monte Carlo method with a constant pressure ensemble is used to study the equation of state of solid hydrogen with translational and rotational degrees of freedom.
同时考虑分子的平动与转动自由度，用等温等压系综的路径积分蒙特卡罗方法研究了固体氢的状态方程。
By applying Feynman path integral method, the second virial coefficient of an ideal and of an interaction anyon gas in a magnetic field are calculated directly in the paper.
用费曼路径积分方法直接计算外磁场中理想任意子气体和相互作用任意子气体的第二维里系数。
The exact analytical equation for the effect AB is worked out by the method path integral.
本文用路径积分方法导出了AB效应的精确解析式。
Using the path integral method for handling the anomaly problem under the comoving representation, we present a unified scheme for deriving the bononization of fermion fields in (1+1) dimensions.
本文利用随动表象下处理反常问题的路径积分方法，给出（1+1）维空间费米场玻色化的统一推导方案。
A numerical path integral solution method is proposed to calculate the response statistics of the moored vessel.
提出了一个数值路径积分解法来计算该艘船舶的响应统计。
Aim to establish the path independent integral and its dual form of energy type, and to determine the singularity order of stresses near the crack tip in plane quasicrystals.
目的建立平面准晶中能量型路径守恒积分及其对偶形式，并确定准晶裂纹体裂尖应力奇异性阶数。
In this paper the theorem in which a curve integral is independent of the integral path on a single connected region is generalized.
本文把在单连通区域上成立的曲线积分与路线无关性定理推广到复连通区域。
The discrete formulas were presented and optimized to improve numerical accuracy and reduce the integral path sensitivity.
指出沿积分方向通过单元中心线的积分路径为最佳 ，计算精度最高。
An ordinary definite integral is defined over a line segment, whereas a line integral may use a more general path, such as a parabola or a circle.
普通定义的积分是定义在一段线段上的，而线积分则用更一般的路径，像抛物线或圆。
The results showed the path independence of J integral of welded joint. It established the foundation of application of elastic plastic J integral in welded structures.
计算结果表明了焊接接头中J积分的路径无关性，并为焊接结构中弹塑性J积分的应用奠定了基础。
It is justified that the integral of the gauge potential along path of not only electron but also scalar particle or spinor particle will contribute a geometric phase factor.
证明了规范场不仅沿入射电子在复连通区域运动路径的积分，而且还可沿入射标量或其他旋量粒子之一在复连通区域的运动路径积分，各自都将贡献一几何相因子。
The basic principle of the path integral formulation for scalar wave propagation in random media is described.
本文叙述了随机介质中标量波传播的路积分解的基本依据。
Using the path integral approach, we obtain the action of this system.
运用相干态路径积分，我们得到了该系统的作用量。
The Lagrangian formulation of the critical dynamics is recovered in the second order approximation of fluctuations in the closed time path continuous integral.
在闭路连续积分中取涨落二级近似，得到临界动力学的拉氏场论表述。
Two basic methods of solution of the Fokker-Planck equation, i. e. the method of the representation of eigenfunction and that of the path integral, are discussed.
本文讨论了福克-普朗克方程的两种基本解法，即本征函数展开和路径积分方法。
The expression of energy release rate is deduced by means of the path-independent M-integral, and corresponding numerical results are given.
利用与路径无关的M积分导出能量释放率表达式并给出相应的数值解。
The supportive environment provided by a spiritual community is an integral part of the path.
由灵修社群提供的支持性环境，是解脱道次第不可或缺的一部份。
Moreover, the difference of J-integral values increases with the increasing of the load and strength mismatching difference and the path-enclosed length of interface between weld metal and base metal.
载荷越大，焊缝与母材的强度差别越大；积分路径中包含的焊缝与母材界面长度越大，J积分的差值越大。
The equation of state of dense hydrogen plasma were calculated by Direct Path Integral Monte Carlo approach.
采用直接蒙特卡洛路径积分方法计算了稠密氢等离子体的物态方程。
The equation of state of dense hydrogen plasma were calculated by Direct Path Integral Monte Carlo approach.
采用直接蒙特卡洛路径积分方法计算了稠密氢等离子体的物态方程。
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