Group Theory: Reducible and Irreducible Representations

This lecture covers the concept of group theory applied to quantum physics, focusing on reducible and irreducible representations. It explains the invariance under continuous symmetries, conservation laws, and internal operations within a group. The lecture also delves into the properties of group elements, commutativity, subgroups, and the representation of a group on a set of operators. It discusses the identity element, parity, and the notion of reducibility, including equivalent representations and completely reducible representations. The lecture concludes with the irreducible representations and the concept of a representation being invertible.