Math For Quantum Chromodynamics And The Electroweak Theory

Mathematics Behind the Standard Model and Particle Physics: Quarks, Leptons, Gauge Bosons, Baryons, Mesons, et al.

What you'll learn

Quantum Chromodynamics

Electroweak Theory

Spontaneous Symmetry Breaking

The Higgs Mechanism

Understand the fundamentals of the Standard model

How quarks compose other particles such as baryons and mesons

Local gauge invariance and interactions

Neutral current interactions

Left and right handed fields

Special unitary group in N dimensions ( SU(N) )

basics of asymptotic freedom and confinement in QCD

Colour and flavour of quarks

W and Z bosons

Gauge covariant derivative

Weinberg angle

gluons

Requirements

Lagrangian field theory

Covariant formulation of Classical electrodynamics

Basics of Quantum Field Theory

Tensors and Special Relativity

Familiarity with the Dirac equation would be beneficial (not strictly necessary, but if you comply with the other prerequisites above, chances are you have already come across the Dirac equation)

Description

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!

Overview

Section 1: Introduction

Lecture 1 Introduction

Lecture 2 Some material for the course

Section 2: Important properties of the Dirac equation, Charge conservation, and SU(N)

Lecture 3 Considerations on the Dirac equation and Dirac matrices

Lecture 4 Dirac equation derived from a lagrangian

Lecture 5 Charge conservation law from Dirac equation

Lecture 6 Important properties of unitary matrices and group theory

Section 3: Quantum Chromodynamics

Lecture 7 Special unitary group in 3 dimensions

Lecture 8 Why local gauge invariance

Lecture 9 Commutator of covariant derivatives

Lecture 10 QCD: the mathematics of quarks and gluons

Lecture 11 Lagrangian for QCD

Lecture 12 Considerations on the QCD Lagrangian: asymptotic freedom and confinement

Section 4: Electroweak theory

Lecture 13 Introduction to the Electroweak Theory

Lecture 14 Left and right handed spinors

Lecture 15 Local gauge invariance for the electroweak theory

Lecture 16 Field strengths in the electroweak theory

Lecture 17 Charged current interactions

Lecture 18 Neutral current interactions

Lecture 19 Derivation of the quark charges

Section 5: Spontaneous symmetry breaking and the Higgs mechanism

Lecture 20 Spontaneous symmetry breaking

Lecture 21 The Higgs mechanism part 1

Lecture 22 The Higgs mechanism part 2

Lecture 23 The Higgs mechanism part 3

Section 6: Appendix

Lecture 24 Conserved current in electromagnetism

physicists,master's level students in physics (or advanced undergraduates),mathematicians,physics enthusiasts,math enthusiasts,scientists,computational scientists,quantum engineers,anyone who is eager to discover the mathematical beauty of the universe