ABSTRACT
This chapter explores the possibility of requiring all interactions to be invariant under independent rotations of the isotopic spin at all space time points. It begins the discussion of local non-Abelian symmetries with the local SU(2) case. The chapter introduces the main ideas of the non-Abelian SU(2) gauge theory which results from the demand of invariance, or covariance, under transformations. It uses the language of isospin when referring to the physical states and operators, bearing in mind that this will eventually mean weak isospin. A simple way of arriving at the desired quantity is to consider the commutator of two covariant derivatives. There is no completely covariant way of selecting out just the two physical components of a massless polarization vector, from the four originally introduced precisely for reasons of covariance. In fact, when gauge quanta appear as virtual particles in intermediate states in Feynman graphs, they will not be restricted to having only two polarization states.
