Algebraic Structures of Degenerate Systems, Physical Requirements and the Indefinite Metric

Abstract

The basic algebraic structures of systems with a gauge degeneracy have been developed in a C’ - algebra framework in [1], of which the present work is a natural extension. We consider the treatment of algebraic conditions in more detail, as well as the compatibility conditions between a given constraint set and a given set of physical transformations. A list of reasonable physical requirements on the algebraic structure is given. We also consider the existence and structure of indefinite inner product representations and obtain various results for obtaining an indefinite inner product representation.