  C. N. Yang's ideas about local gauge symmetry and non-integrable phases have
been enormously fertile sources of inspiration in fundamental physics and in
the quantum theory of matter. They also arise naturally in describing the
dynamics of deformable bodies. Here I extend previous discussions of the gauge
symmetry of deformable bodies in several directions, bringing in an arbitrary
number of dimensions, general time-dependence, conservation laws and adiabatic
residuals. I briefly indicate other potential applications of the conceptual
framework.
