Effective Constraints for Quantum Systems

Abstract

An effective formalism for quantum constrained systems is presented which allows manageable derivations of solutions and observables, including a treatment of physical reality conditions without requiring full knowledge of the physical inner product. Instead of a state equation from a constraint operator, an infinite system of constraint functions on the quantum phase space of expectation values and moments of states is used. The examples of linear constraints as well as the free non-relativistic particle in parameterized form illustrate how standard problems of constrained systems can be dealt with in this framework.

40 pages

References in corpus (18)

• Loop Quantum Cosmology
• Partial and Complete Observables for Hamiltonian Constrained Systems
• Partial and Complete Observables for Canonical General Relativity
• Isotropic Loop Quantum Cosmology
• Effective Equations of Motion for Quantum Systems
• Anomaly freedom in perturbative loop quantum gravity
• Loop quantum gravity corrections to gravitational wave dispersion
• Large scale effective theory for cosmological bounces
• Quantum Gravity and Higher Curvature Actions
• Dynamical coherent states and physical solutions of quantum cosmological bounces
• Quantum nature of cosmological bounces
• Cosmological vector modes and quantum gravity effects
• Effective equations for isotropic quantum cosmology including matter
• Coordinate time dependence in Quantum Gravity
• Recollapsing quantum cosmologies and the question of entropy
• On the geometry of quantum constrained systems
• Poisson Geometry in Constrained Systems
• On obtaining classical mechanics from quantum mechanics

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