Representations of SU(2): Symmetries and Transformations

This lecture discusses the representations of the SU(2) group, focusing on two-dimensional representations and their properties. The instructor explains how these representations can take values such as plus or minus one-half and how they relate to vector representations. The lecture covers the transformation of tensors and the significance of symmetric and anti-symmetric combinations in these representations. The instructor illustrates how to construct fully symmetric states and discusses the implications of tensor products in quantum mechanics. The concept of irreducible representations is introduced, along with the importance of understanding how these representations transform under symmetries. The lecture also touches on the construction of invariant Lagrangians and the role of left-handed and right-handed spinors in building these invariants. Throughout the lecture, the instructor emphasizes the mathematical framework necessary to understand the behavior of fields and their transformations, providing a comprehensive overview of the subject matter.