The study of non Abelian gauge theories is thought to be in the realm of quantum field theory, having to do mainly with the study of elementary particle phenomena. The non Abelian gauge theory widely known as the ”standard model” describes correctly all elementary particles and forces except gravity.
Our goal here is to show that non Abelian gauge theories appear also in physical settings in which the field need not be quantized (second quantization). Hence they can be considered as classical fields which are the subject of this book. In particular it will be shown that those fields appear in the study of molecular systems is the frame work of the Born - Oppenheimer theory.