ABSTRACT
This chapter is concerned with two global non-Abelian symmetries, which lead to useful conservation laws but not to any specific dynamical theory. It begins with the first non-Abelian symmetry to be used in particle physics, the hadronic isospin ‘SU(2) symmetry’ proposed by Heisenberg in the context of nuclear physics, and now understood as following from QCD and the smallness of the quark masses as compared with the QCD scale parameter ΛMS. The chapter then extends this to SU(3)f flavour symmetry. Finally, it introduces the idea of a global chiral symmetry, which is a symmetry of theories with massless fermions. This may be expected to be a good approximate symmetry for the quarks. But the anticipated observable consequences of this symmetry (for example, nucleon parity doublets) appear to be absent.
