Quantum phase transitions from a new class of representations of a diffeomorphism group

Using a technique based on self-similar random processes, we construct unitary representations of the group of diffeomorphisms of R describing continuum quantum systems with infinitely many degrees of freedom. These can describe systems undergoing a phase change, from rarefied to condensed, at the critical value of a correlation parameter. The method offers promise for generalization to higher spatial dimensions, and for application to theories of extended quantum objects.