Effective Constraints for Relativistic Quantum Systems

Details Effective Constraints for Relativistic Quantum Systems Effective Constraints for Relativistic Quantum Systems

2009-06-09

arxiv.org/abs/0906.1772v2

Phys. Rev. D 80 (2009) 125008

Physics

Mathematical Physics

27 pages, 2 figures; v2: new appendix comparing effective constraints and physical coherent states by an example

Scientific paper

10.1103/PhysRevD.80.125008

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.

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