Quantization, coherent states and diffeomorphism groups

We suggest extending the method of coherent-states quantization, which applies to homogeneous spaces for locally compact groups, to the case of infinite-dimensional groups such as diffeomorphism groups. Such a framework could unify a number of different approaches to quantum theory. We review some relevant results and examples, and take a first step in this program by demonstrating that the unitary representation of Diff(R) obtained from the 'single-particle' coadjoint orbit is in fact square-integrable. (orig.)