Effective Constraints for Relativistic Quantum Systems

Understand

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 side-stepping 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 back-reaction, are addressed by the examples studied here.