Details

Format: Lecture and Discussion

Course Material: Textbooks, Reading & Lecture Notes

Evaluation: Attendance & written report (10 pages) on a topic chosen in consultation
with the instructor, plus a 10+5 minute oral presentation of the report to the class.
Texts:

Group Theory in a Nutshell, A. Zee, Princeton Press.

Symmetries in Quantum Physics, U. Fano & A. R. P. Rao, Academic Press.

Symmetry, Broken Symmetry & Topology, M. Guidry & Y. Sun, Cambridge.

Topological Quantum Numbers in Physics, David Thouless, World Scientific.

Cosmic Strings & Topological Defects, A. Velinkin & E. Shellard, Cambridge.

Topics:

Finite, Discrete & Point Groups

Representations of Point Groups

Lie Groups, Lie Algebras & their Representations

Direct Product Spaces  Reducible representations

Symmetry, Symmetry Breaking & Phase transitions

Discrete Symmetries: Parity, TimeReversal & Charge Conjugation

Landau Theory and Lagrangian Field Theories

Topology, Homotopy Groups and Topological Defects

Applications of Group Theory & Topology in QFT

CMT: Liquid Crystals, Ferromagnets & Superconductors

QFT: Mass Generation, Higgs & Gauge Bosons

CMT: Higgs Bosons & Topology of HeliumThree

QFT: Nonequilibrium Phase Transitions

COS: Nucleation of Topological Defects
