The gauge argument: a Noether reason

Why is gauge symmetry so important in modern physics, given that one must eliminate it when interpreting what the theory represents? This chapter offers a discussion of the sense in which gauge symmetry can be fruitfully applied to constrain the space of possible dynamical models in such a way that forces and charges are appropriately coupled. It reviews the most well-known application of this kind, known as the ‘gauge argument’ or ‘gauge principle’; discusses its difficulties, and then reconstructs the gauge argument as a valid theorem in quantum theory. The chapter then presents what the authors take to be a better and more general gauge argument, based on Noether’s second theorem in classical Lagrangian field theory, and argues that this provides a more appropriate framework for understanding how gauge symmetry helps to constrain the dynamics of physical theories.