2 Chiral Symmetry (a) Consider the chiral rotation of a massless Dirac field where 75 is introduced and discussed e.g. in PS section 3.4, and o is an arbitrary real constant. Show that this is a symmetry of the Lagrangian, and find the corresponding Noether current. Show that the corresponding Noether charge measures the total helicity of a collection of massless Dirac particles, and that the addition of a mass term to the Lagrangian violates the symmetry. Find an equation that expresses the violation of current conservation by the mass term in the Lagrangian. (b) Find the Noether current corresponding to charge conservation by considering a phase rotation of a Dirac field (of arbitrary mass)