Posted on Categories:Particle Physics, 物理代写, 粒子物理

## avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

•最快12小时交付

•200+ 英语母语导师

•70分以下全额退款

## 物理代写|粒子物理代写Particle Physics代考|The group SU(3)

In this chapter we shall describe the main properties of the group $S U(3)$ and its representations. As will become clear in the following chapters, $S U(3)$ is related to a symmetry of fundamental importance in particle physics. Here we shall present its mathematical structure.
$S U(3)$ is the group which is isomorphic to that of unitary $3 \times 3$ matrices of determinant equal to $+1$. Thus, the general element $u$ satisfies the conditions
$$u^{\dagger} u=\mathbf{1}=u u^{\dagger} \text { and } \operatorname{det} u=1$$
and, consequently, is characterised by eight real parameters.

## 物理代写|粒子物理代写Particle Physics代考|The representations of $\mathbf SU(3) The representations of$\mathbf{S U ( 3 )}$. To construct the irreducible representations of$S U(3)$and the corresponding Clebsch-Gordan decomposition rules, we shall follow the tensor method used for$S U(2)$. Modulo a few special features of$S U(2)$and the combinatoric complications as we move on to higher groups and representations, the method is applicable to all members of the unitary series and even beyond. • The trivial (singlet) representation 1. As usual, this is the representation in which all elements of the group are represented by the number 1 . • The defining (3) representation. Three complex quantities$\psi^i, i=1,2,3$, are said to be the components of a triplet (3) of$S U(3)$, if they transform according to $$\psi^{i^{\prime}}=u_j^i \psi^i \quad\left(\psi^{\prime}=u \psi\right) \forall u \in S U(3)$$ • The conjugate$\overline{\mathbf{3}}$of the defining representation. Three complex quantities$\chi_i, i=1,2,3$, are defined to be the components of an anti-triplet$\overline{\mathbf{3}}$of$S U(3)$, if they transform according to $$\chi_i^{\prime}=u_i^{\dagger j} \chi_j \quad\left(\chi^{\prime}=\chi u^{\dagger}\right) \forall u \in S U(3)$$ An immediate consequence of this definition is that, if$\psi^i$is a triplet, the complex conjugates$\psi^{i^*}$form an anti-triplet, since then,$\psi^{\dagger}$, whose components are exactly the$\psi^{i *}$, indeed transform according to${\psi^{\prime}}^{\prime}=\psi^{\dagger} u^{\dagger}$. Thus, the consistent notation of the components of$\psi^{\dagger}$is$\psi_i^{\dagger}$with one lower index. Also, notice that given two triplets$\psi$and$\chi$, the quantities$\psi^{\dagger} \chi=\psi^{i *} \chi^i$and its Hermitian conjugate$\chi^{\dagger} \psi$are invariant (singlets) under$S U(3)$. ## 粒子物理代写 ## 物理代写|粒子物理代写Particle Physics代考|The group SU(3) 在本章中，我们将描述组的主要属性$S U(3)$及其表示。正如在以下章节中将变得清楚的那样，$S U(3)$与粒子物理学中具有根本重 要性的对称性有关。这里我们将介绍它的数学结构。$S U(3)$是与酉同构的群$3 \times 3$行列式矩阵等于$+1$. 因此，一般元龶$u$满足条件 $$u^{\dagger} u=\mathbf{1}=u u^{\dagger} \text { and } \operatorname{det} u=1$$ 因此，其特征在于八个实参数。 ## 物理代写|粒子物理代写Particle Physics代考|The representations of \$\mathbf $\mathrm{SU}(3)$

• 平凡 (单线态) 表示 1 . 像往常一样，这是组中所有元表都由数字 1 表示的表示。
• 定义 (3) 表示。三复数 $\psi^i, i=1,2,3$, 被称为是三元组 (3) 的组成部分 $S U(3)$, 如果他们根据
$$\psi^{i^{\prime}}=u_j^i \psi^i \quad\left(\psi^{\prime}=u \psi\right) \forall u \in S U(3)$$
• 共轭 $\overline{\mathbf{3}}$ 的定义表示。三西数 $\chi_i, i=1,2,3$, 被定义为反三元組的分量 $\overline{\mathbf{3}}$ 的 $S U(3)$ ，如果他们根据
$$\chi_i^{\prime}=u_i^{\dagger j} \chi_j \quad\left(\chi^{\prime}=\chi u^{\dagger}\right) \forall u \in S U(3)$$
这个定义的直接结果是，如果 $\psi^i$ 是三元组，里共轭 $\psi^{i^*}$ 形成一个反三元组，从那时起， $\psi^{\dagger}$ ，其分量恰好是 $\psi^{i *}$ ，确实根据 $\psi^{\prime \prime}=\psi^{\dagger} u^{\dagger}$. 因此，组件的一致表示法 $\psi^{\dagger}$ 是 $\psi_i^{\dagger}$ 个较低的指数。
另外，请注意给定两个三元组 $\psi$ 和 $\chi$, 数量 $\psi^{\dagger} \chi=\psi^{i *} \chi^i$ 及其厄米特共轭 $\chi^{\dagger} \psi$ 在下是不变的（单线态) $S U(3)$.

## 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。

Posted on Categories:Particle Physics, 物理代写, 粒子物理

## avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

•最快12小时交付

•200+ 英语母语导师

•70分以下全额退款

## 物理代写|粒子物理代写Particle Physics代考|Scattering in Classical and Quantum Physics

Almost every act of observation involves a scattering experiment. In everyday life it is usually the scattering of visible light by the object under study and its resolution is limited by the light’s wavelength. During the last century the quest for higher resolution forced us to abandon light as a probe and, following Rutherford’s pioneering experiment, to use more and more energetic particle beams. Today all information we have about the structure of matter at the deepest accessed level comes from high energy scattering experiments. The probes are particles we can accelerate, which are essentially protons (or ions) and electrons. A particle accelerator is, in fact, a “microscope” whose spatial resolution is determined by its maximum energy. The CERN Large Hadron Collider ( $\mathrm{LHC})$, with proton beams up to $7 \mathrm{TeV}$, has a resolution reaching $10^{-19} \mathrm{~m},{ }^{1}$ and is today – in 2021 – the most powerful microscope man has ever built. In this chapter we shall introduce the basic concepts necessary to describe and understand the results of scattering experiments in particle physics. Only the main ideas will be presented, with no detailed proofs. Some of the proofs are proposed as exercises at the end of the chapter.

## 物理代写|粒子物理代写Particle Physics代考|The Scattering Cross Section

We start by considering the case of two colliding particles. The laboratory frame is defined to be the reference frame in which one of these particles, called the target, is at rest. The other is the projectile. By contrast, in the centre of mass reference frame nothing distinguishes the target from the beam. ${ }^{2}$

In the simplest case a projectile, idealised as a hard sphere of radius $r$ in straight motion, will hit the target, a sphere of radius $R$, if the trajectory of the centre of the projectile intersects the disk of radius $r+R$ perpendicular to it and centred at the centre of the target. The surface area of this disk, $\sigma_{\text {tot }}=\pi(r+R)^{2}$, is called the total cross section of this collision process.

In actual experiments the situation is more complex. First, we are not interested only in collisions of hard spheres. Even in classical physics we may want to compute the results of scattering among particles interacting through a potential, for example two electrically charged particles. Second, we do not usually consider the collision of just one particle against another. We send, instead, a beam of particles against a target containing many particles and place a detector in the direction $\Omega(\theta, \phi)$ with an acceptance of $\mathrm{d} \Omega$, which counts the number of particles $\mathrm{d} \mathcal{N}(\Omega) / \mathrm{d} \Omega$ going through it per unit solid angle and per unit time. We want to extract out of such a measurement a quantity, like the cross section we introduced previously, which refers to the collision of one particle in the beam and one particle in the target.

## 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。