ABSTRACT
This chapter discusses the most fundamental symmetry properties of particle physics in context of such specially chosen models. A quantum field in general is an assembly of an infinite number of interacting harmonic oscillators. Excitations of such oscillators are associated with particles. Perhaps the most important discovery of modern particle physics is the gauge principle. According to it, all interactions in nature arise from the claim that the Lagrangian has to be invariant under local symmetry transformations, that is symmetry rotations that may be different at different space-time points. It is remarkable that this claim predicts the low energy structure of the Lagrangian. The chapter examines certain classical systems, and explores results in the language of particle theory. There are lots of different possibilities at the molecular level leading to the same low energy picture. The study of the dynamics of gauge fields is the most important problem of modern physics.
