Construction of quantum Dirac observables and the emergence of WKB time

2019/10/31 by Leonardo Chataignier
Mathematics · Physics and Astronomy · #Classical mechanics #Coupling constant #De Sitter universe #Dirac (video compression format) #Initial singularity #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Observable #Physics #Quantum #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Quantum dynamics #Quantum mechanics #Singularity #Theoretical physics #Universe #WKB approximation #gr-qc #hep-th #quant-ph

paper · pdf · doi:10.1103/physrevd.101.086001

published as Phys. Rev. D 101, 086001 (2020) · v2: references updated, minor typos corrected, title slightly changed, conceptual clarifications added, published in Physical Review D

openalex publication_date 2020/04/01 · arxiv created 2020/04/04 · arxiv updated 2020/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We describe a method of construction of gauge-invariant operators (Dirac observables or ``evolving constants of motion'') from the knowledge of the eigenstates of the gauge generator in time-reparametrization invariant mechanical systems. These invariant operators evolve unitarily with respect to an arbitrarily chosen time variable. We emphasize that the dynamics is relational, both in the classical and quantum theories. In this framework, we show how the ``emergent Wentzel-Kramers-Brillouin time'' often employed in quantum cosmology arises from a weak-coupling expansion of invariant transition amplitudes, and we illustrate an example of singularity avoidance in a vacuum Bianchi I (Kasner) model.

Citations

• The semiclassical approximation to quantum gravity
• Quantization of Gauge Systems
• Quantum spacetime of a charged black hole
• Semiclassical Gravity and the Problem of Time
• Quantum canonical transformations. Physical equivalence of quantum theories
• Generalized Hamiltonian Dynamics
• Mathematical Formulation of the Quantum Theory of Electromagnetic Interaction
• The theory of gravitation in Hamiltonian form
• The Use of the Proper Time in Quantum Electrodynamics I
• Constraints in Covariant Field Theories
• Generalized Hamiltonian dynamics
• Quantum Theory of Gravity. I. The Canonical Theory
• Observables in effective gravity
• Time in quantum gravity: An hypothesis
• Partial and complete observables for Hamiltonian constrained systems
• TIME AND INTERPRETATIONS OF QUANTUM GRAVITY
• Republication of: The dynamics of general relativity
• Life in an energy eigenstate: Decoherent histories analysis of a model timeless universe
• Partial and Complete Observables for Canonical General Relativity
• Quantum-gravitational effects on gauge-invariant scalar and tensor perturbations during inflation: The de Sitter case
• A change of perspective: switching quantum reference frames via a perspective-neutral framework
• Group Averaging and Refined Algebraic Quantization: Where are we now?
• Non-Inertial Frames and Dirac Observables in Relativity
• Refined Algebraic Quantization: Systems with a single constraint
• Canonical Quantum Gravity and the Problem of Time