Isolated systems and their symmetries, part II: Local and global symmetries of field theories

Physical theories, for the most part, should be understood as modelling isolated subsystems of a larger universe; doing so, among other benefits, greatly clarifies the interpretation of the dynamical symmetries of those theories. Building on a general framework for the symmetries of isolated systems developed in the prequel to this paper, I apply that framework to field theory. The resultant analysis provides a general basis for interpreting the physical significance of symmetries according to their topological and asymptotic features: global symmetries in general, and local symmetries insofar as they preserve boundary conditions and are asymptotically nonvanishing and/or topologically nontrivial, can be understood as physical transformations of an isolated system against the assumed background of other systems. Other symmetries in general must be understood as mere redescription, though in certain circumstances even non-boundary-preserving local symmetries can be afforded physical significance. The analysis largely reproduces - and so can be seen as a theoretical justification for - general practice in contemporary physics.