ABSTRACT
This chapter shows the advantages of using the chiral 2-sphere as a model. It is simpler than the chiral SU(2) × SU(2) scheme, even in the purely bosonic sector. Moreover, the 2-sphere is a Kahler manifold and so admits a supersymmetric extension in which the Goldstone bosons acquire fermionic (Weyl) partners without yet more quasi-Goldstone bosons and fermions being forced into the model. The chapter provides a treatment of most of the basic mathematics at the root of the subject of this book. Curiously, it considers the embedding of the structure needed for the current problem into that of a larger system that has previously been solved in general coordinates leading to a closed form involving only simple functions.
