Higher time derivatives in effective equations of canonical quantum systems

Abstract

Quantum-corrected equations of motion generically contain higher time derivatives, computed here in the setting of canonically quantized systems. The main example in which detailed derivations are presented is a general anharmonic oscillator, but conclusions can be drawn also for systems in quantum gravity and cosmology.

26 pages

References in corpus (10)

• Towards singularity and ghost free theories of gravity
• Anomaly-free scalar perturbations with holonomy corrections in loop quantum cosmology
• Stable bounce and inflation in non-local higher derivative cosmology
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• Large scale effective theory for cosmological bounces
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• How quantum is the big bang?
• Effective equations for isotropic quantum cosmology including matter
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• Protected $SL(2,\mathbb{R})$ Symmetry in Quantum Cosmology
• Minisuperspace models as infrared contributions
• The BKL scenario, infrared renormalization, and quantum cosmology
• Canonical description of cosmological backreaction
• Anomaly freedom in perturbative models of Euclidean loop quantum gravity
• Effective constraint algebras with structure functions
• Effective Field Theory of Loop Quantum Cosmology
• Fluctuation energies in quantum cosmology
• Factor ordering and large-volume dynamics in quantum cosmology
• A loop quantum multiverse?
• Electric Time in Quantum Cosmology
• Deformed covariance in spherically symmetric vacuum models of loop quantum gravity: Consistency in Euclidean and self-dual gravity
• Semiclassical States on Lie Algebras
• Canonical derivation of effective potentials
• Multi-field inflation from single-field models
• Quasiclassical solutions for static quantum black holes
• Black-hole models in loop quantum gravity