Quantum Field Theory: Conservation Laws

This lecture focuses on deriving conserved currents in classical field theory and quantum field theory, emphasizing the importance of symmetries and equations of motion. The instructor explains the difference between conserved quantities in classical mechanics and field theory, highlighting the role of Noether's theorem. Through detailed mathematical derivations, the lecture covers the application of symmetries to Lagrangians, transformations of fields under translations, and the conservation of currents. The instructor also provides insights into the significance of infinitesimal shifts in coordinates and the implications of Gal's theorem. By exploring the relationship between symmetries, Lagrangians, and conserved currents, the lecture offers a comprehensive understanding of the fundamental principles underlying quantum field theory.