General relativity histories theory I: The spacetime character of the canonical description
arXiv:gr-qc/0306034 · doi:10.1088/0264-9381/21/2/020
Abstract
The problem of time in canonical quantum gravity is related to the fact that the canonical description is based on the prior choice of a spacelike foliation, hence making a reference to a spacetime metric. However, the metric is expected to be a dynamical, fluctuating quantity in quantum gravity. We show how this problem can be solved in the histories formulation of general relativity. We implement the 3+1 decomposition using metric-dependent foliations which remain spacelike with respect to all possible Lorentzian metrics. This allows us to find an explicit relation of covariant and canonical quantities which preserves the spacetime character of the canonical description. In this new construction, we also have a coexistence of the spacetime diffeomorphisms group, and the Dirac algebra of constraints.
23 pages, submitted to Class. Quant. Grav
References in corpus (5)
Cited by in corpus (18)
- Partial and Complete Observables for Hamiltonian Constrained Systems
- Beables/Observables in Classical and Quantum Gravity
- Change in Hamiltonian General Relativity from the Lack of a Time-like Killing Vector Field
- Linear Positivity and Virtual Probability
- Emergent Semiclassical Time in Quantum Gravity. I. Mechanical Models
- Problem of Time and Background Independence: the Individual Facets
- Gravitational effects in macroscopic quantum systems: a first-principles analysis
- General relativity histories theory II: Invariance groups
- Minisuperspace Models in Histories Theory
- Approaching the Problem of Time with a Combined Semiclassical-Records-Histories Scheme
- On the Semiclassical Approach to Quantum Cosmology
- Covariance and Time Regained in Canonical General Relativity
- The thermodynamics of self-gravitating systems in equilibrium is holographic
- Possible Anthropic Support for a Decaying Universe: A Cosmic Doomsday Argument
- Multi-Time Measurements in Hawking Radiation: Information at Higher-Order Correlations
- Gravitational backreaction in cosmological spacetimes
- How black holes store information in high-order correlations
- Phase Space Representations and Perturbation Theory for Continuous-time Histories