# Available student project - Lie algebras in particle physics

## Research fields

- Physics of the Nucleus
- Theoretical Physics

## Project details

In the 1930s, Eugene Wigner noted that there seemed to be a link between the symmetries of a quantum system and the representation theory of certain algebraic groups. Since then, the deep connections between the representations of Lie groups and the properties of quantum field theories (i.e. the dynamics of elementary particles) have been well-established. Indeed, modern gauge theories such as the Standard Model which describe the underlying nature of the universe are intrinsically reliant on the mathematical properties of the representations of groups like *SU*(*n*), the special unitary group. In particular, the famous "quark model" arises in a strikingly natural way when studying the decomposition of *SU*(*3*) representations.

In this reading course, students will learn about the links between Lie group representations and particle physics by studying Howard Georgi's "*Lie Groups in Particle Physics: From Isospin to Unified Theories*", doing set exercises, and learning how the quark model arises in the aforementioned manner. This course will be appropriate for theory-minded physics students, particularly those with an interest in quantum field theory or nuclear physics, or maths students with an interest in the application of abstract algebra to the physical world.

## Required background

Knowledge of linear algebra is required, and some familiarity with abstract algebra is preferred. Familiarity with quantum mechanics is also necessary.

## Project suitability

- 3rd year special project
- PhB (2nd or 3rd year)