Algebraic quantum gravity (AQG): I. Conceptual setup

By K. Giesel, T. Thiemann. 2006

162 citations recorded by the source corpus.

We introduce a new top down approach to canonical quantum gravity, called algebraic quantum gravity (AQG). The quantum kinematics of AQG is determined by an abstract *-algebra generated by a countable set of elementary operators labelled by an algebraic graph. The quantum dynamics of AQG is governed by a single master constraint operator. While AQG is inspired by loop quantum gravity (LQG), it differs drastically from it because in AQG there is fundamentally no topology or differential structure. A natural Hilbert space representation acquires the structure of an infinite tensor product (ITP) whose separable strong equivalence class Hilbert subspaces (sectors) are left invariant by the quantum dynamics. The missing information about the topology and differential structure of the spacetime manifold as well as about the background metric to be approximated is supplied by coherent states. Given such data, the corresponding coherent state defines a sector in the ITP which can be identified with a usual QFT on the given manifold and background. Thus, AQG contains QFT on all curved spacetimes at once, possibly has something to say about topology change and provides the contact with the familiar low energy physics. In particular, in two companion papers we develop semiclassical perturbation theory for AQG and LQG and thereby show that the theory admits a semiclassical limit whose infinitesimal gauge symmetry agrees with that of general relativity. In AQG everything is computable with sufficient precision and no UV divergences arise due to the background independence of the fundamental combinatorial structure. Hence, in contrast to lattice gauge theory on a background metric, no continuum limit has to be taken. There simply is no lattice regulator that must be sent to zero.

Subfields: Neurology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a62c3c5cb0c74556d1f34ccdb7ae8ed74b2c646c

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Citations in the corpus

Anomaly freedom in perturbative loop quantum gravity (2008, background): “Some rare solvable systems can be studied by exact effective equations without truncation, which in cosmology is realized for a flat isotropic model sourced by a free, massless scalar [6].”
Quantum graphity: A model of emergent locality (2008, background): “Another possibility for incorporating matter and indeed gravitational degrees of freedom in the graph-based model that is worth mentioning is via the approach of algebraic quantum gravity [18].”
Scalar material reference systems and loop quantum gravity (2012, methodology): “The authors nevertheless claim that they can treat their model with the methods from [26] without having to care about the spatial diffeomorphism constraint anymore and nevertheless describe the physical sector of the theory.”
Phase space descriptions for simplicial 4D geometries (2008, background): “Our analysis opens the question of how the dynamics defined, for instance, via the Hamiltonian constraints in LQG [6] or the ‘master constraint’ in algebraic quantum gravity [46] interacts with the gluing constraints.”
Flipped spinfoam vertex and loop gravity (2007, methodology): “Numerous approaches to quantum gravity start from the assumption of a fundamental spacetime discreteness ([ 47 ]); others use spacetime discreteness as a regularization”
Loop Quantum Gravity (2003, methodology): “• Uniform discretization Motivated by the same problems as those considered by Giesel and Thiemann in [134], Campiglia, Di Bartolo, Gambini and Pullin have studied a lattice formulation of the fundamental theory, denoted “uniform discretization” [82].”