EXTENDED COHERENT STATES AND PATH-INTEGRALS WITH AUXILIARY VARIABLES

The usual construction of coherent states allows a wider interpretatio n in which the number of distinguishing state labels is no longer mini mal; the label measure determining the required resolution of unity is then no longer unique and may even be concentrated on manifolds with positive co-dimension. Paying particular attention to the residual res trictions on the measure, we choose to capitalize on this inherent fre edom and in formally distinct ways, systematically construct suitable sets of extended coherent states which, in a minimal sense, are charac terized by auxiliary labels. Interestingly, we find these states lead to path integral constructions containing auxiliary (essentially uncon strained) path-space variables. The impact of both standard and extend ed coherent state formulations on the content of classical theories is briefly examined, the latter showing the existence of new, and genera lly constrained, classical variables. Some implications for the handli ng of constrained classical systems are given, with a complete analysi s awaiting further study.