物理代写|粒子物理代写Particle Physics代考|PHYC90011 Conservation laws – baryon and lepton number

如果你也在 怎样代写粒子物理Particle Physics PHYC90011这个学科遇到相关的难题,请随时右上角联系我们的24/7代写客服。粒子物理Particle Physics或高能物理学是对构成物质和辐射的基本粒子和力量的研究。宇宙中的基本粒子在标准模型中被分为费米子(物质粒子)和玻色子(载力粒子)。费米子有三代,但普通物质只由第一代费米子构成。第一代包括形成质子和中子的上下夸克,以及电子和电子中微子。已知由玻色子介导的三种基本相互作用是电磁力、弱相互作用和强相互作用。

粒子物理Particle Physics夸克不能单独存在,而是形成强子。含有奇数夸克的强子被称为重子,含有偶数夸克的强子被称为介子。两个重子,质子和中子,构成了普通物质的大部分质量。介子是不稳定的,寿命最长的介子只持续了几百分之一微秒的时间。它们发生在由夸克组成的粒子之间的碰撞之后,例如宇宙射线中快速移动的质子和中子。介子也会在回旋加速器或其他粒子加速器中产生。

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物理代写|粒子物理代写Particle Physics代考|PHYC90011 Conservation laws – baryon and lepton number

物理代写|粒子物理代写Particle Physics代考|Conservation laws – baryon and lepton number

We know from experiment that there exist quantities whose values remain constant in all physical processes. In classical physics we have encountered conserved quantities such as energy, momentum or angular momentum. We have seen that they are related to the assumed invariance of the equations of motion under translations and rotations. There exist also conserved quantities that are not related to any symmetry transformations of space-time. The most common example is the electric charge. This conservation law has many observable consequences. Let us mention two which apply, in particular, to particle physics:

  • In a reaction of the form $A_1+A_2+\ldots \rightarrow B_1+B_2+\ldots$, in which a set of initial particles, the $A$ s, gives, through their interactions, a set of final particles, the $B$ s, the algebraic sum of the electric charges of the $A$ s is equal to that of the $B \mathrm{~s}$.
  • The electron, being the lightest of all electrically charged particles, is absolutely stable. The current limit is $\tau_e \geq 6.6 \times 10^{28}$ years.

Already in classical electromagnetic theory the conservation of the electric charge is a consequence of the equations of motion. Experiments in particle physics show the existence of additional conserved charges, although they are not sources of any macroscopic external field. We shall present two examples in this section and we shall have a more complete discussion later.

The baryon number. 11 In 1932 we could define this conserved charge as corresponding to the number of the particles we called “nucleons” in Table 6.1. They are the proton and the neutron. Although, as we saw already, in nuclear reactions a neutron can turn into a proton, or vice versa, we have never observed a reaction in which the number of nucleons is not conserved. For example, we never observed a proton decaying as $p \rightarrow e^{+}+\gamma$, although this would have been allowed by electric charge conservation. ${ }^{12}$ We conclude that we can assign to each particle in the table a new charge, which can take positive, negative or zero values, such that in every reaction the algebraic sum of the charges remains the same in the initial and the final state. In 1932, we could have called this new charge the nucleon number, but, anticipating what will come next, we call it the baryon number $B$. Among the particles in Table $6.1$, nucleons are assigned the value $B=1$, (we shall call them baryons), anti-nucleons the value $B=-1$, while all other particles have $B=0$. Baryon number has the same properties as the electric charge, namely that it is conserved, baryons can be produced in baryon-anti-baryon pairs and the lightest baryon, the proton, is stable. The difference is that, as we have said already, baryon number is not the source of a classical field.

The lepton number. ${ }^{13}$ In complete analogy we can define a new quantum number $L$ with $L=1$ for the electron and the neutrino, $L=-1$ for the positron and the antineutrino and $L=0$ for all other particles. All experiments show that $L$ is conserved in every reaction.

物理代写|粒子物理代写Particle Physics代考|The four fundamental interactions

In order to understand the structure of matter, a knowledge of the elementary constituents is not enough. We should supplement it with that of the interactions among them. Although our ideas on the nature of the elementary particles evolved considerably during the twentieth century, those on the fundamental interactions have remained remarkably unchanged. In all scales, from that of the elementary particles to that of the universe as a whole, the structure of matter is due to four fundamental interactions. One of the main subjects of this book is to describe their detailed properties, but, for the purposes of this discussion, it will be sufficient to classify them according to two simple parameters, whose understanding does not require any knowledge of quantum field theory. They are: (i) the strength of the interaction and, (ii) its range. These concepts were introduced in Chapter 4 , when we discussed scattering from a non-relativistic potential, but we can also adopt a purely phenomenological viewpoint. In a decreasing strength order, we can list the interactions as follows:

The strong interactions. They are mainly responsible for nuclear structure. Indeed, we have explained already that the various nuclei are bound states of protons and neutrons. Each proton carries one unit of positive electric charge and, therefore, protons are subject to electrostatic repulsion. The remarkable cohesion of nuclei shows the existence of attractive forces among protons and neutrons, which must be much stronger to outweigh the electrostatic repulsion. We know experimentally that strong interactions have a short range, typically on the order of a few times $10^{-13} \mathrm{~cm}$, and their effects are not manifest in everyday life. Not all known particles are subject to strong interactions. Those that are, are called hadrons. ${ }^{14}$ Among the particles of Table $6.1$, the nucleons are, naturally, hadrons but all other particles, namely electrons, neutrinos and photons, are not. ${ }^{15}$ Following the terminology we used in the last section, we will call the matter particles that are not hadrons i.e. electrons and neutrinos, leptons. Understanding the nature of the strong interactions has been a long-lasting problem in high energy physics. Its solution has offered deep insight into the laws of nature, insight that far exceeds the domain of nuclear forces. We shall give a brief description of these ideas later in this book.

The electromagnetic interactions. They are responsible for the atomic and molecular structure. They have long range and their effects are observable at macroscopic scales. We mentioned in Chapter 2 that the electromagnetic interactions, expressed order by order in perturbation theory, can be viewed as the results of the exchange of virtual photons, the quanta of the electromagnetic field, between electrically charged particles. We also saw in Chapter 4 that the long range is attributed to the zero mass of the photon.

The weak interactions. They are responsible for nuclear $\beta$-decay as well as the decays of other unstable particles. To give a measure of how weak the weak interactions are, we note that, experimentally, neutrinos, which have no strong or electromagnetic interactions, are produced at the centre of stars and escape from them without being absorbed. For a very massive star, neutrino radiation is the only known cooling mechanism. We know today that weak interactions share many common features with the electromagnetic ones. They are also due to the exchange of virtual quanta, the weak vector bosons $W^{+}, W^{-}$and $Z$. However, these quanta are massive and, as a result, the weak interactions are of short range. Naturally, the existence of these weak interaction intermediaries was unknown in 1932. In this book we shall explore this weak-electromagnetic analogy much further.

The gravitational interactions. Their importance in both terrestrial and cosmic phenomena is well known but, at the microscopic level, their effects are too weak to be observable. We shall not discuss them much further in this book.

物理代写|粒子物理代写Particle Physics代考|PHYC90011 Conservation laws – baryon and lepton number

粒子物理代写

物理代写|粒子物理代写PARTICLE PHYSICS代考|CONSERVATION LAWS – BARYON AND LEPTON NUMBER


我们从实验中知道,存在其值在所有物理过程中保持不变的量。在经典物理学中,我们遇到过能量、动量或角动量等守恒量。我们已经看到它们与平移和旋转运动 方程的假定不变性有关。还存在与时空的任何对称变换无关的守恒量。最常见的例子是电荷。这个守恒定律有许多可观察到的结果。让我们提到两个特别适用于粒
在经典电磁理论中,电荷守恒是运动方程的结果。粒子物理实验表明存在额外的守恒电荷,尽管它们不是任何宏观外场的来源。我们将在本节中提供两个示例,稍
重子数。 11 在 1932 年,我们可以将这种守恒电荷定义为对应于我们在表 $6.1$ 中称为“核子”的粒子的数量。它们是质子和中子。虽然,正如我们已经看到的,在核反 应中,中子可以变成质子,反之亦然,但我们从末观牢到核子数量不守恒的反应。例如,我们从末观察到质子衰变为 $p \rightarrow e^{+}+\gamma$ ,尽管电荷守恒允许这样做。 12 我们得出结论,我们可以为表中的每个粒子分配一个新电荷,该电荷可以取正值、负值或零值,这样在每个反应中,电荷的代数和在初始和最终状态下保持相同。 在 1932 年,我们可以将这种新电荷称为核子数,但是,考虑到接下来会发生什么,我们将其称为重子数 $B$. 在表中的粒子中 $6.1$, 核子被赋值 $B=1$, weshallcallthembaryons, 反核子值 $B=-1$ ,而所有其他粒子都有 $B=0$. 重子数与电荷具有相同的性质,即它是守恒的,重子可以在重子-反重子对中产生,最
轻子数。 ${ }^{13}$ 在完全类比中,我们可以定义一个新的量子数 $L$ 和 $L=1$ 对于电子和中微子, $L=-1$ 对于正电子和反中微子和 $L=0$ 对于所有其他粒子。所有实验表明
为了理解物质的结构,仅了解基本成分是不够的。我们应该用它们之间的相互作用来补充它。尽管我们对基本粒子性质的看法在 20 世纪有了很大的发展,但对基 本相互作用的看法却一直保持着显着的变化。在所有尺度上,从基本粒子的尺度到整个宇宙的尺度,物质的结构都归因于四种基本相互作用。本书的主要主题之一 是描述它们的详细属性,但是为了讨论的目的,根据两个简单的参数对它们进行分类就足够了,理解这些参数不需要任何量子场论知识。他们是: $i$ 相互作用的强 度, $i i$ 它的范围。这些概念在第 4 章中介绍过,当时我们从非相对论势讨论散射,但我们也可以采用纯现象学的观点。按照强度递减的顺序,我们可以列出相互作

物理代写|粒子物理代写PARTICLE PHYSICS代考|THE FOUR FUNDAMENTAL INTERACTIONS


强相互作用。它们主要负责核结构。事实上,我们已经解释过各种原子核是质子和中子的束缚态。每个质子携带一个单位的正电荷,因此,质子受到静电排斥。原 子核显着的凝聚力表明质子和中子之间存在吸引力,这种吸引力必须强得多才能超过静电排斥力。我们通过实验知道强相互作用的范围很短,通常是几倍的数量级 $10^{-13} \mathrm{~cm}$ ,它们的影响在日常生活中并不明显。并非所有已知粒子都受到强相互作用。那些是,被称为强子。 ${ }^{14}$ 表中粒子6.1,核子自然是强子,但所有其他粒 子,即电子、中微子和光子,都不是。 ${ }^{15}$ 按照我们在上一节中使用的术语,我们将把不是强子的物质粒子(即电子和中微子)称为轻子。理解强相互作用的本质一 直是高能物理学中一个长期存在的问题。它的解决方案提供了对自然法则的深刻洞察,远超核力领域的洞尓力。我们将在本书后面对这些想法进行简要说明。
电磁相互作用。它们负责原子和分子结构。它们的射程很远,而且它们的影响在宏观尺度上是可以观察到的。我们在第 2 章中提到,在微扰理论中逐次表示的电磁
弱相互作用。他们负责核 $\beta$-衰变以及其他不稳定粒子的衰变。为了衡量弱相互作用有多弱,我们注意到,在实验中,没有强相互作用或电磁相互作用的中微子是在 恒星中心产生的,并在没有被吸收的情况下从恒星中逸出。对于一颗非常大的恒星,中微子辐射是唯一已知的冷却机制。我们今天知道,弱相互作用与电磁相互作 用有许多共同特征。它们也是由于虚拟量子的交换,弱矢量玻色子 $W^{+}, W^{-}$和 $Z$. 然而,这些量子是巨大的,因此,弱相互作用是短程的。当然,这些弱相互作用 中介体的存在在 1932 年还不为人知。在本书中,我们将更深入地探讨这种弱电磁类比。
引力相互作用。它们在地球和宇宙现象中的重要性是众所周知的,但在微观层面上,它们的影响太弱以至于无法观察到。我们不会在本书中进一步讨论它们。

物理代写|粒子物理代写Particle Physics代考

物理代写|粒子物理代写Particle Physics代考 请认准UprivateTA™. UprivateTA™为您的留学生涯保驾护航。

微观经济学代写

微观经济学是主流经济学的一个分支,研究个人和企业在做出有关稀缺资源分配的决策时的行为以及这些个人和企业之间的相互作用。my-assignmentexpert™ 为您的留学生涯保驾护航 在数学Mathematics作业代写方面已经树立了自己的口碑, 保证靠谱, 高质且原创的数学Mathematics代写服务。我们的专家在图论代写Graph Theory代写方面经验极为丰富,各种图论代写Graph Theory相关的作业也就用不着 说。

线性代数代写

线性代数是数学的一个分支,涉及线性方程,如:线性图,如:以及它们在向量空间和通过矩阵的表示。线性代数是几乎所有数学领域的核心。

博弈论代写

现代博弈论始于约翰-冯-诺伊曼(John von Neumann)提出的两人零和博弈中的混合策略均衡的观点及其证明。冯-诺依曼的原始证明使用了关于连续映射到紧凑凸集的布劳威尔定点定理,这成为博弈论和数学经济学的标准方法。在他的论文之后,1944年,他与奥斯卡-莫根斯特恩(Oskar Morgenstern)共同撰写了《游戏和经济行为理论》一书,该书考虑了几个参与者的合作游戏。这本书的第二版提供了预期效用的公理理论,使数理统计学家和经济学家能够处理不确定性下的决策。

微积分代写

微积分,最初被称为无穷小微积分或 “无穷小的微积分”,是对连续变化的数学研究,就像几何学是对形状的研究,而代数是对算术运算的概括研究一样。

它有两个主要分支,微分和积分;微分涉及瞬时变化率和曲线的斜率,而积分涉及数量的累积,以及曲线下或曲线之间的面积。这两个分支通过微积分的基本定理相互联系,它们利用了无限序列和无限级数收敛到一个明确定义的极限的基本概念 。

计量经济学代写

什么是计量经济学?
计量经济学是统计学和数学模型的定量应用,使用数据来发展理论或测试经济学中的现有假设,并根据历史数据预测未来趋势。它对现实世界的数据进行统计试验,然后将结果与被测试的理论进行比较和对比。

根据你是对测试现有理论感兴趣,还是对利用现有数据在这些观察的基础上提出新的假设感兴趣,计量经济学可以细分为两大类:理论和应用。那些经常从事这种实践的人通常被称为计量经济学家。

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。

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