Math for Quantum Chromodynamics and the Electroweak theory

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!

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Frequently Asked Questions

How long do I have access to the course materials?

You can view and review the lecture materials indefinitely, like an on-demand channel.

Can I take my courses with me wherever I go?

Definitely! If you have an internet connection, courses on Udemy are available on any device at any time. If you don’t have an internet connection, some instructors also let their students download course lectures. That’s up to the instructor though, so make sure you get on their good side!