Effective constraints for relativistic quantum systems

Determining the physical Hilbert space is often considered the most difficult but crucial part of completing the quantization of a constrained system. In such a situation it can be more economical to use effective constraint methods, which are extended here to relativistic systems as they arise for instance in quantum cosmology. By sidestepping explicit constructions of states, such tools allow one to arrive much more feasibly at results for physical observables at least in semiclassical regimes. Several questions discussed recently regarding effective equations and state properties in quantum cosmology, including the spreading of states and quantum backreaction, are addressed by the examples studied here.