### 物理代写|高能物理代写High Energy Physics代考|PHYS557

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|高能物理代写High Energy Physics代考|Gravitation as a Fundamental Interaction

Many textbooks begin with a discussion of the classical gravitational force between two macroscopic masses $m_1$ and $m_2$
$$F_{\mathrm{G}}=-G_{\mathrm{N}} \frac{m_1 m_2}{r^2}$$
where $G_{\mathrm{N}}$ is Newton’s gravitational constant and $r$ the distance between the masses. With a view to formulating the description of gravitation as an elementary interaction, where the particles exchange a “graviton” (Table 1.1) and from which the law of Newtonian gravitation should result, dimensional analysis of Newton’s equation shows that $G_{\mathrm{N}}$ is not dimensionless, a fundamental requirement for the construction of an elementary theory. That is why a “gravitational fine structure constant” is commonly defined by $\alpha_{\mathrm{G}}=G_{\mathrm{N}} m_{\mathrm{p}}^2 / \hbar c$ on an energy scale equal to the mass of the proton (the quantity that appears in Table 1.1). But by the tiny numerical value of $\alpha_{\mathrm{G}} \sim 10^{-38}$, gravitation can almost always be ignored compared to the other forces of Nature, at least as long as we talk about elementary processes. The question that arises is: why is it then that gravitation dominates the structure of the observable Universe, stars, and galaxies? The simplest answer is to be found in the unique nature of the “charge” of the gravitational field, which is just mass: if macroscopic sets of particles are considered, gravitation “accumulates” until the structure itself is dominated by it, while the other forces cancel each other out as we consider more and more particles. Let us consider quantitatively $N$ particles of equal mass. The radius of a sphere formed by this set of particles depends on $N^{1 / 3}$, while the energy of the gravitational bond is proportional to $N^{2 / 3}$. To compensate for the smallness of the factor of $10^{-38}$ of the constant $\alpha_{\mathrm{G}}$, the number of particles required must be $N=10^{38 \times(3 / 2)}=10^{57}$. This is approximately the number of particles (protons) in a star like our own, with mass denoted by $M_{\odot}$, and results in the “natural” scale where gravitation becomes more important than the other forces at a macroscopic scale (in fact we know that the Sun, for example, does not have a large contribution to its binding energy from strong, weak, and electromagnetic interactions) [7].

This discussion leads to the conclusion that we can neglect gravitation in microscopic systems, unless the energy scale grows as much as to make $\alpha_{\mathrm{G}} \approx 1$. Under these conditions, microscopic gravitation would be as important as the other fundamental interactions. The mass where this equivalence occurs is
$$m_{\mathrm{Pl}}=\left(\frac{\hbar c}{G_{\mathrm{N}}}\right)^{1 / 2}$$ the so-called Planck mass, with associated energy $E_{\mathrm{Pl}}=m_{\mathrm{PI}} \times c^2=10^{19} \mathrm{GeV}$. As the most energetic phenomena in the laboratory, and even in the extreme cosmic rays of ultra-high energy discussed in Chap. 12, are still many orders of magnitude below this value, we will never have to worry about gravitation as an elementary theory, i.e., its quantum version. This is fortunate, since we do not yet have a consistent theory of quantum gravitation. Although the basic contribution should be the exchange diagram of an intermediate particle (or graviton) between any two massive particles, no quantum calculation is fully consistent. On the other hand, the classical versions of Newtonian gravitation and General Relativity have had spectacular success. Although we would like to have a quantum theory of gravitation, it has never been possible to build an acceptable version. When proceeding in the same way as in the quantization of other field theories, there is a divergence of the quantum theory of gravitation above a certain order in standard perturbation theory. Many physicists believe that there is a strong analogy here with the history of weak interactions, since Fermi’s quantized theory also leads to divergent results beyond a certain order in perturbation theory. It may be that Einstein’s theory of gravitation is not a fundamental theory, but only an “effective” theory, akin to the Fermi case. Thus, physicists still live in a dual world where they know that, on the one hand, the microscopic world is described by the laws of Quantum Mechanics, and on the other, gravitation behaves in a classical way as far as we can measure and observe, and these two descriptions are incompatible. The solution of this antagonism is what motivates the search for unified theories.

## 物理代写|高能物理代写High Energy Physics代考|Role of Weak Interactions

In the 19th century, thanks to contributions from Maxwell, Faraday, and others, Electromagnetism was established as a theoretical paradigm for the study of phenomena involving electric charges in the laboratory. The discovery of the electron by J.J. Thompson in 1897 (the quantum of electric charge par excellence) provided a way to “penetrate” the atom by throwing electrons at it, and later to discover the atomic nucleus using helium nuclei (also electrically charged) as projectiles. The observation of the behavior and composition of atomic nuclei then opened an important window in the study of elementary particles.

By the 1920s, the proton had been identified as a component of the Rutherford nucleus. A series of experiments showed that, under certain circumstances, a nucleus could change its state of charge, with the expulsion of an electron from the nucleus. Thus, there were two possibilities: either the atomic nucleus contained electrons, or they were emitted by a particle decaying into a proton and an electron. This last hypothesis received definitive confirmation when Chadwick discovered the neutron in 1931. It was found that neutrons could spontaneously convert into protons, either when free or within the nucleus, whence Nature could change the type of nucleon that constituted the nucleus under certain conditions.

It also became clear that the observed conversion was not of electromagnetic origin (although the electric charge was conserved). Physicists thus sought the origin and nature of the force responsible. In the first place, it had to be a short-range force because the reaction takes place mainly on scales of the order of the atomic nucleus. The characterization of the strength of this force also emerged from the data, and turned out to be several orders of magnitude weaker than the electromagnetic force (see Table 1.1). Thus, the discovery of weak forces associated neutron decay with a new fundamental interaction:
$$\mathrm{n} \rightarrow \mathrm{p}+\mathrm{e}^{-}+\overline{\mathrm{v}}_{\mathrm{e}}$$
where the neutron and proton were still part of the nucleus, and the electron escaped from the nuclear region. The last protagonist here, in fact an anti-neutrino, was not observed at first, but was postulated by W. Pauli to solve two serious problems with this decay: the conservation of energy and the conservation of angular momentum in the reaction. In fact, in spontaneous decay, such as was observed for neutrons within nuclei, the total angular momentum did not seem to be conserved, since the neutron spin $(1 / 2)$ was equal to half the spin of the particles observed in the reaction products, a proton of spin $1 / 2$ and an electron of spin 1/2. Moreover, the sum of the energies of the particles taking part in the reaction was not constant. Nobody liked to abandon the conservation of energy and the angular momentum in Physics, and this is what inspired Pauli’s creative solution to this problem.

## 物理代写|高能物理代写高能物理学代考|引力作为一种基本相互作用

$$F_{\mathrm{G}}=-G_{\mathrm{N}} \frac{m_1 m_2}{r^2}$$

$$m_{\mathrm{Pl}}=\left(\frac{\hbar c}{G_{\mathrm{N}}}\right)^{1 / 2}$$所谓的普朗克质量，其相关能量是$E_{\mathrm{Pl}}=m_{\mathrm{PI}} \times c^2=10^{19} \mathrm{GeV}$。由于实验室中最有能量的现象，甚至在第十二章讨论的超高能量的极端宇宙射线中，仍然比这个值低许多个数量级，我们永远不必担心万有引力作为一个基本理论，即它的量子版本。这是幸运的，因为我们还没有一个一致的量子引力理论。尽管基本贡献应该是任意两个大质量粒子之间的中间粒子(或引力子)的交换图，但没有任何量子计算是完全一致的。另一方面，牛顿万有引力和广义相对论的经典版本已经取得了巨大的成功。尽管我们希望有一个量子引力理论，但一直不可能建立一个可接受的版本。当按照其他场论的量子化方法进行时，标准摄动理论中引力的量子化理论在某一阶以上存在发散。许多物理学家认为这与弱相互作用的历史有很强的相似之处，因为费米的量子化理论也会导致超出摄动理论某一阶的发散结果。爱因斯坦的引力理论可能不是一个基本理论，而只是一个“有效”理论，类似于费米案例。因此，物理学家仍然生活在一个双重世界中，他们知道，一方面，微观世界是由量子力学定律描述的，另一方面，万有引力在我们可以测量和观察的范围内以经典的方式表现，这两种描述是不兼容的。这种对抗性的解决是对统一理论的探索的动力

## 物理代写|高能物理代写High Energy Physics代考|弱相互作用的作用

$$\mathrm{n} \rightarrow \mathrm{p}+\mathrm{e}^{-}+\overline{\mathrm{v}}_{\mathrm{e}}$$
，其中中子和质子仍然是原子核的一部分，电子从核区域逃逸。这里的最后一个主角，实际上是一个反中微子，一开始并没有被观察到，但W.泡利假设它解决了这个衰变的两个严重问题:反应中的能量守恒和角动量守恒。事实上，在自发衰变中，例如在原子核中观察到的中子，总角动量似乎并不是守恒的，因为中子自旋$(1 / 2)$等于在反应产物中观察到的粒子自旋的一半，一个自旋为$1 / 2$的质子和一个自旋为1/2的电子。此外，参与反应的粒子的能量之和不是恒定的。没有人愿意放弃物理学中的能量守恒和角动量，这就是激发泡利创造性地解决这一问题的原因

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。