J. A. Sauls

**Lectures:** January 4 - March 8

**When:** Monday, Wednesday 11:30 am - 1:00 pm

**Where:** Room: L158, Tech Institute

Symmetry, topology and geometry are central elements of physical theories spanning all known length and energy scales. Group theory plays an important role in atomic, nuclear, high-energy and condensed matter physics. Spontaneous symmetry breaking, phase transitions, and the emergence of quantized excitations and topological defects - from phonons and quantized vortices to Higgs Bosons and cosmic strings - are rooted in symmetry groups and their representations describing the quantum theory of matter and radiation.

This is a two-quarter sequence covering the symmetry and topology in quantum mechanics, quantum field theory and condensed matter physics. The course starts with an introduction to group theory covering finite groups and Lie groups with applications ranging from selection rules for atomic transitions to the role of symmetry and group representations in the theory of phase transitions. The course will cover homotopy groups and their application to the theory of topological defects and excitations in broken symmetry states of matter and quantum fields.

- Groups, Sub-Groups, Co-sets, Classes
- Representation Theory
- Finite Groups and their Representations
- Rotations, Reflections, Parity and Time-Reversal
- Lie Groups and their Representations
- Symmetry, Symmetry Breaking & Phase transitions
- Topology, Homotopy Groups and Topological Defects
- Applications in Condensed Matter and Quantum Field Theory

File translated from T

On December 8, 2016.