Description

This research project explores the profound role played by Lie groups and Lie algebras in particle theory. In particular, Lie groups in theoretical physics are the fundamental concept when discussing the group of continuous symmetry of a given Lagriangian model. For example, when discussing the mathematical foundation of gauge theories that describe the strong, weak, and electromagnetic forces we encounter the Lie groups: SU(3), SU(2), and U(1). This project dives into how these symmetries dictate particle interactions, conservation laws, and possibly the structure of the Standard Model.

A central aim of the project is to investigate the classification and representation theory of Lie groups with particular emphasis towards the role they play in high-energy physics. For the more mathematically inclined students, it is also possible to discuss more in depth about the representation theory of Lie groups and Cartan's classification.

Pre- Co-requisites

2H Mathematical Physics or equivalently Theoretical Physics II. (Lagrangian formulation and intro to Quantum mechanics)

3H Quantum Mechanics or equivalently Foundations of Physics 2A.

3H Geometry of Mathematical Physics.

Resources

For some background:

• Read the wikipedia article on Lie groups.

Reading material.

• Lie Algebras in Particle Physics , H.Georgi, Frontiers in Physics.