Symmetries in Quantum Field Theory

This lecture delves into the symmetries in quantum field theory, focusing on the transformational properties of different components. The instructor explains the transformation rules under various symmetries, such as rotations and boosts, and how they affect the different indices. The lecture covers the concept of Casimir operators and their role in labeling states within representations. It also explores reducible representations of the Poincare group, emphasizing the use of invariant operators to label states. The discussion extends to the significance of Casimir products and the strategy employed to find reducible representations. The lecture concludes with a detailed analysis of the little group transformations and their impact on the states' properties.