Quantum Field Theory: Exercises on QFT1

This lecture covers exercises related to quantum field theory, focusing on ladder operators, invariant measures under Lorentz transformations, Lorentz invariance of Noether charges, custodial symmetry, and vacuum stability. Students will compute commutation relations, demonstrate invariance under Lorentz transformations, and analyze the Lorentz invariance of Noether charges in various field theories. The lecture also explores the Hamiltonian in momentum space, Fourier expansions for scalar fields, and the algebra of ladder operators. Additionally, it delves into the Lorentz invariance of Noether charges and the constraints for obtaining a reasonable theory in the context of custodial symmetry and vacuum stability.