Perturbative quantum evolution of the gravitational state and dressing in general backgrounds
arXiv:2209.06836 · doi:10.1103/PhysRevD.110.026012
Abstract
This paper sets up a perturbative treatment of the evolving quantum state of a gravitational system, in a Schrödinger-like picture, working about a general background. This connects gauge symmetry, the constraints, gravitational dressing, and evolution. Starting with a general time slicing, we give a simple derivation of the relation between the constraints, the hamiltonian, and its well-known boundary term. Among different approaches to quantization with constraints, we focus on a "gauge-invariant canonical quantization," which is developed perturbatively in the gravitational coupling. The leading-order solution of the constraints (including the Wheeler-DeWitt equation) for perturbations about the background is given in terms of an explicit construction of gravitational dressings built using certain generalized Green functions; different such dressings corresponding to adding propagating gravitational waves to a particular solution of the constraints. Dressed operators commute with the constraints, expressing their gauge invariance, and have an algebraic structure differing significantly from the undressed operators of the underlying field theory. These operators can act on the vacuum to create dressed states, and evolution of general such states is then generated by the boundary hamiltonian, and alternately may be characterized using other relational observables. This provides a concrete approach to studying perturbative time evolution, including the leading gravitational backreaction, of quantum states of black holes with flat or anti de Sitter asymptotics, for example on horizon-crossing slices. This description of evolution in turn provides a starting point for investigating possibly important corrections to quantum evolution, that go beyond quantized general relativity.
arXiv comment24 pages + refs. v2: improved treatment of constraints, added appendix on constraints generating gauge transformations, update on connection to other work, other small improvements v3: minor clarifications in response to referee comments
References in corpus (57)
- The Dynamics of General Relativity
- Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory
- The Gravitational Hamiltonian, Action, Entropy, and Surface Terms
- Relative entropy equals bulk relative entropy
- Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
- An Algebra of Observables for de Sitter Space
- Second-order Perturbations of the Friedmann World Model
- Observables in effective gravity
- Space from Hilbert Space: Recovering Geometry from Bulk Entanglement
- Gravity and the Crossed Product
- Stability of Black Holes and Black Branes
- Diffeomorphism-invariant observables and their nonlocal algebra
- Gauge transformations in the Lagrangian and Hamiltonian formalisms of generally covariant theories
- Observables, gravitational dressing, and obstructions to locality and subsystems
- Gravitational Observables and Local Symmetries
- The Off-Shell Black Hole
- On the Generality of Refined Algebraic Quantization
- Functional Evolution of Free Quantum Fields
- Black holes, quantum information, and unitary evolution
- Unitarity and Holography in Gravitational Physics
- Nonviolent nonlocality
- Models for unitary black hole disintegration
- Decoding the hologram: Scalar fields interacting with gravity
- Construction of Bulk Fields with Gauge Redundancy
- How is quantum information localized in gravity?
- Nonviolent unitarization: basic postulates to soft quantum structure of black holes
- Dirac Constraint Quantization of a Dilatonic Model of Gravitational Collapse
- Bulk Entanglement Gravity without a Boundary: Towards Finding Einstein's Equation in Hilbert Space
- The Structure of the Gravitational Action and its relation with Horizon Thermodynamics and Emergent Gravity Paradigm
- Holography from the Wheeler-DeWitt equation
- Gravitational dressing, soft charges, and perturbative gravitational splitting
- Gravitational splitting at first order: Quantum information localization in gravity
- Unitarity and ultraviolet regularity in cosmology
- Boundary unitarity and the black hole information paradox
- A uniqueness criterion for the Fock quantization of scalar fields with time dependent mass
- Gauge-invariant quantum gravitational corrections to correlation functions
- Gauge-invariant observables, gravitational dressings, and holography in AdS
- Cosmological perturbation theory and quantum gravity
- Quantum-first gravity
- Hilbert space structure in quantum gravity: an algebraic perspective
- Universal quantum mechanics
- Non-commutative Geometry from Perturbative Quantum Gravity
- Propagators for gauge-invariant observables in cosmology
- Holography without strings?
- Black holes in the quantum universe
- Uniqueness of the Fock quantization of scalar fields under mode preserving canonical transformations varying in time
- One-loop quantum gravitational corrections to the scalar two-point function at fixed geodesic distance
- On the questions of asymptotic recoverability of information and subsystems in quantum gravity
- A "black hole theorem," and its implications
- Quantum evolution of the Hawking state for black holes
- One-loop quantum gravitational backreaction on the local Hubble rate
- Schrödinger evolution of the Hawking state
- Holography and unitarity
- Self-Adjointness in Klein-Gordon Theory on Globally Hyperbolic Spacetimes
- Schrödinger evolution of two-dimensional black holes
- Non-commutative Geometry from Perturbative Quantum Gravity in de Sitter spacetime
- Synchronous coordinates and gauge-invariant observables in cosmological spacetimes