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.