Talk on group theory and field theory

Synopsis

Group theory plays a fundamental role in modern physics, providing the mathematical framework for understanding symmetries in field theories. In this talk, we will explore how field theories can be constructed from group theory for general groups.

We will begin with an overview of representation theory for finite groups, introducing key concepts and their relevance in physical systems. Moving beyond ordinary representations, we will discuss projective representations and their connection to the second cohomology group, which plays a crucial role in classifying symmetries of fermions in Kitaev’s periodic table. If time permits, we will further explore how these ideas extend to continuous symmetries, deepening our understanding of their role in field theory.