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# 物理代写|粒子物理代写Particle Physics代考|PHYC90011 Heisenberg and the Symmetries of Nuclear Forces

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## 物理代写|粒子物理代写Particle Physics代考|Heisenberg and the Symmetries of Nuclear Forces

As we have noted already, 1932, the year of the discovery of the neutron, is the year when nuclear physics started taking its present form. Of course, the transition from the old nuclear model of protons and electrons to the modern one of protons and neutrons was not instantaneous. It took several years for the new paradigm to be generally accepted. What is less known is that the same year marks another revolution in our understanding of the fundamental interactions, which is closely related to the new nuclear model. It is the introduction of the concept of internal symmetries, a concept that introduced into theoretical physics a degree of abstraction not easy to grasp intuitively. The original idea is due to W. Heisenberg but, as we shall explain briefly later, the actual history is more complicated. We shall present the idea using our present understanding and we shall comment on the historical developments at the end.

We are used to the fact that particles may carry internal degrees of freedom. An electron at rest is described by two orthogonal states in the Hilbert space, the $|\uparrow\rangle$ with spin projection $+\frac{1}{2}$ and the $|\downarrow\rangle$ with spin projection $-\frac{1}{2}$. They satisfy the orthogonality relation $\langle\uparrow \mid \downarrow\rangle=0$. Normally, we could have invented two different names to describe these two states. Nevertheless, we talk about one electron and the reason why this is correct is that there exist transformations which leave the equations of motion invariant and transform one state to the other. Indeed, if the spin projections are taken along the $z$-axis, a rotation of $180^{\circ}$ around any axis in the $x-y$ plane interchanges $|\uparrow\rangle$ and $|\downarrow\rangle$.

## 物理代写|粒子物理代写Particle Physics代考|Fermi and the Weak Interactions

Already in 1926 , before the introduction of the Schrödinger wave equation, Fermi had published two papers with the statistical rules which established Fermi quantum statistics and gave fermions their name. In 1933, he came back with one of the most influential papers in particle physics in which he proposed a field theory model for the $\beta$-decay of neutrons. Even today, when this theory has been superseded by the Standard Model of electroweak interactions, which we shall develop in this book, Fermi’s theory is still used as a good low energy approximation.

This paper contains many revolutionary ideas. Fermi was one of the first physicists who believed in the physical existence of the neutrino. Contrary to Heisenberg, in the Bohr-Pauli controversy Fermi sided clearly with the second. But he went further and broke completely with the prevailing philosophy, according to which particles that come out from a nucleus ought to be present inside it. ${ }^{22}$ In his paper he formulated the full quantum field theory for fermion fields and introduced the formalism of creation and annihilation operators, the analogue of the ones we used for the electromagnetic field in equations (2.23)and (2.24). It was the first time that quantised fermion fields appeared in particle physics. We shall give a full account of this formalism in Chapter 10 where we shall also indicate the novel features that Fermi introduced in order to incorporate Fermi statistics. The paper appeared at the beginning of 1934 in Italian ${ }^{23}$ under the title Tentativo di una teoria della emissione di raggi $\beta$.

## 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。