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所在平台: Udemy |
课程主页: https://www.udemy.com/course/math-for-quantum-chromodynamics-and-the-electroweak-theory/
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课程名称：量子色动力学与电弱理论的数学 课程概述：掌握粒子物理背后的数学！欢迎参加本课程，我们将为您揭示驱动两个基本粒子物理理论的数学：量子色动力学（QCD）和电弱理论。 您将学习的内容： - **狄拉克方程**：熟悉这个对于理解夸克和电子等粒子至关重要的方程。我们将从复杂标量场的经典场论出发，推广理论以获得狄拉克方程。 - **SU(N) 基础**：我们将进行SU(N)群的实践和理论探索，这是量子物理中的一个关键概念，也是标准模型的基础。 - **理解相互作用**：我们将解构粒子相互作用，揭示规范协变导数在解读量子力学中的作用。规范不变性将是与粒子相互作用密切相关的另一个重要主题。例如，我们将看到电荷粒子的局部规范不变性必然要求光子的存在及电磁相互作用！这个概念也将应用于QCD和电弱理论中。 - **深入研究QCD**：探讨强相互作用，作为粒子物理中的一个主要力量，以及描述夸克和胶子的重要数学基础。 - **电弱理论**：了解电磁力和弱核力如何结合在一起，提供一个简单、清晰的介绍。其数学描述将帮助我们理解受到电弱力作用的轻子和夸克的行为。轻子和夸克的家族在课程中会逐渐讨论，学生会随着课程的进展而更加熟悉这些概念。 - **希格斯场**：研究希格斯场，其负责为Z和W玻色子赋予质量，并探索其数学方面。这是标准模型方程的必要步骤，因为为了保持方程的某种对称性，W和Z玻色子不能具有质量。希格斯场，尤其是所谓的“自发对称性破缺”，将允许Z和W玻色子获得质量。 - **构建数学直觉**：我们的教学方法优先考虑深刻理解而非复杂公式，确保您真正掌握这些概念。 通过本课程，您将牢固掌握支持这些先进粒子物理理论的数学框架。无论您是物理爱好者还是希望增强基础的学生，本课程都将为您提供进入量子色动力学和电弱理论迷人世界的工具。立即注册，开始您对粒子物理数学核心的探索之旅！
Master the Mathematics Behind Particle Physics!Welcome to a course that aims to demystify the math driving two essential particle physics theories: Quantum Chromodynamics (QCD) and Electroweak Theory.What You'll Learn:The Dirac Equation: Get comfortable with this vital equation, crucial for understanding particles like quarks and electrons. We will start from the classical field theory of a complex scalar field and generalize the theory to obtain the Dirac equation. SU(N) Basics: We'll kick off with a practical and theoretical exploration of SU(N) groups, a key concept in quantum physics and the foundation of the Standard model.Understanding Interactions: We'll break down particle interactions, uncovering the role of gauge covariant derivatives in deciphering quantum forces. Gauge invariance will be another essential topic related to particle interactions. For instance: we'll see how the local gauge invariance of the theory for electrically charged particles requires the existence of the photon and of the electromagnetic interaction! This concept will also be applied to QCD and the Electroweak theory.Dive into QCD: Explore the strong force, a major player in particle physics, and its mathematical foundation for the description of quarks and gluons.Electroweak Theory: Understand how electromagnetism and the weak nuclear force come together in this simple, clear introduction. Its mathematical description will allow us to understand the behavior of leptons and quarks subjected to the electroweak force. The families of leptons and quarks will be discussed little by little during the course; the student will become more and more familiar as the course progresses.The Higgs Field: We'll examine the Higgs field, responsible for granting particles such as the Z and W bosons mass, and explore its mathematical aspects. This is a necessary step towards the equations of the standard model, since, in order to preserve a certain symmetry in the equations, the W and Z bosons are not allowed to have mass. The Higgs field, and in particular the so-called "Spontaneous Symmetry Breaking", will allow the Z and W bosons to acquire mass.Building Mathematical Intuition: Our approach prioritizes deep comprehension over complex formulas, ensuring you truly grasp the concepts.By the end of this course, you'll have a solid grasp of the mathematical framework supporting these advanced particle physics theories. Whether you're a physics enthusiast or a student seeking to strengthen your foundation, this course equips you with the tools to navigate the captivating world of Quantum Chromodynamics and Electroweak Theory.Enroll now and embark on your journey into the mathematical core of particle physics!
