  The idea then is that we have various representations of some physical structure which may be transformed or translated into one another, and then we have an invariant state under such transformations which represents the objective state of affairs. The group structure is primary and the group representations constructed from this structure have a derivative status. Representations are extraneous to physical states but they allow our empirical knowledge of them. Objects are picked out by the identification of invariants with respect to the transformations relevant to the context. Thus, on this view, elementary particles are hypostatisations of sets of quantities that are invariant under the symmetry groups of particle physics.