# Algebraic Quantum Gravity (AQG). I. Conceptual Setup

@article{Giesel2007AlgebraicQG, title={Algebraic Quantum Gravity (AQG). I. Conceptual Setup}, author={Kristina Giesel and Thomas Thiemann}, journal={Classical and Quantum Gravity}, year={2007}, volume={24}, pages={2465-2497} }

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…

## Tables from this paper

## 138 Citations

Algebraic quantum gravity (AQG): IV. Reduced phase space quantization of loop quantum gravity

- Physics
- 2010

We perform a canonical, reduced phase space quantization of general relativity by loop quantum gravity (LQG) methods. The explicit construction of the reduced phase space is made possible by the…

Hilbert space structure in quantum gravity: an algebraic perspective

- Physics
- 2015

A bstractIf quantum gravity respects the principles of quantum mechanics, suitably generalized, it may be that a more viable approach to the theory is through identifying the relevant quantum…

Algebraic quantum gravity (AQG): II. Semiclassical analysis

- Physics, Mathematics
- 2007

In the previous paper (Giesel and Thiemann 2006 Conceptual setup Preprint gr-qc/0607099) a new combinatorial and thus purely algebraical approach to quantum gravity, called algebraic quantum gravity…

Algebraic quantum gravity (AQG): III. Semiclassical perturbation theory

- Mathematics
- 2006

In the two previous papers of this series we defined a new combinatorical approach to quantum gravity, Algebraic Quantum Gravity (AQG). We showed that AQG reproduces the correct infinitesimal…

On the relation of canonical and covariant formulations of Loop Quantum Gravity

- Physics
- 2015

Loop Quantum Gravity (LQG) is a background independent approach towards a quantum theory of gravity that splits into a canonical and a covariant branch the latter of which is also often called spin…

Projective Loop Quantum Gravity I. State Space

- Mathematics
- 2014

Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski to describe quantum states as projective families of density matrices…

Quantum dyanmics of loop quantum gravity

- Physics
- 2007

In the last 20 years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. The aim of loop quantum gravity is to…

A curvature operator for LQG

- Mathematics
- 2014

Loop Quantum Gravity [1] is a promising candidate to finally realize a quantum description of General Relativity. The theory presents two complementary descriptions based on the canonical and the…

Lessons for Loop Quantum Gravity from Parametrised Field Theory

- Mathematics
- 2010

In a series of seminal papers, Laddha and Varadarajan have developed in depth the quantisation of Parametrised Field Theory (PFT) in the kind of discontinuous representations that are employed in…

Quantum Cauchy surfaces in canonical quantum gravity

- Physics, Mathematics
- 2015

For a Dirac theory of quantum gravity obtained from the refined algebraic quantization procedure, we propose a quantum notion of Cauchy surfaces. In such a theory, there is a kernel projector for the…

## References

SHOWING 1-10 OF 108 REFERENCES

Algebraic quantum gravity (AQG): II. Semiclassical analysis

- Physics, Mathematics
- 2007

In the previous paper (Giesel and Thiemann 2006 Conceptual setup Preprint gr-qc/0607099) a new combinatorial and thus purely algebraical approach to quantum gravity, called algebraic quantum gravity…

Algebraic quantum gravity (AQG): III. Semiclassical perturbation theory

- Mathematics
- 2006

In the two previous papers of this series we defined a new combinatorical approach to quantum gravity, Algebraic Quantum Gravity (AQG). We showed that AQG reproduces the correct infinitesimal…

Quantum spin dynamics (QSD): VI. Quantum Poincaré algebra and a quantum positivity of energy theorem for canonical quantum gravity

- Mathematics, Physics
- 1997

We quantize the generators of the little subgroup of the asymptotic Poincare group of Lorentzian four-dimensional canonical quantum gravity in the continuum. In particular, the resulting ADM energy…

Quantum spin dynamics (QSD): VII. Symplectic structures and continuum lattice formulations of gauge field theories

- Mathematics
- 2001

Interesting nonlinear functions on the phase spaces of classical field theories can never be quantized immediately because the basic fields of the theory become operator-valued distributions.…

Gauge field theory coherent states (GCS): IV. Infinite tensor product and thermodynamical limit

- Mathematics, Physics
- 2001

In the canonical approach to Lorentzian quantum general relativity in four spacetime dimensions an important step forward has been made by Ashtekar, Isham and Lewandowski some eight years ago through…

Quantum theory of geometry: I. Area operators

- Mathematics
- 1996

A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated…

Quantum spin dynamics (QSD) V: Quantum Gravity as the natural regulator of the Hamiltonian constraint of matter quantum field theories

- Physics
- 1998

It is an old speculation in physics that, once the gravitational field is successfully quantized, it should serve as the natural regulator of infrared and ultraviolet singularities that plague…

QSD III : Quantum Constraint Algebra and Physical Scalar Product in Quantum General Relativity

- Mathematics
- 1997

This paper deals with several technical issues of non-perturbative four-dimensional Lorentzian canonical quantum gravity in the continuum that arose in connection with the recently constructed…

Quantum spin dynamics: VIII. The master constraint

- Mathematics
- 2006

Recently the master constraint programme (MCP) for loop quantum gravity (LQG) was launched which replaces the infinite number of Hamiltonian constraints by a single master constraint. The MCP is…

Quantum spin dynamics (QSD): IV. ? Euclidean quantum gravity as a model to test ? Lorentzian quantum gravity

- Physics
- 1997

The quantization of Lorentzian or Euclidean 2 + 1 gravity by canonical methods is a well studied problem. However, the constraints of 2 + 1 gravity are those of a topological field theory and…