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 describi ng 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 meth od offers promise for generalization to higher spatial dimensions, and for application to theories of extended quantum objects.