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

@article{Giesel2006AlgebraicQG, title={Algebraic quantum gravity (AQG): III. Semiclassical perturbation theory}, author={Kristina Giesel and Thomas Thiemann}, journal={Classical and Quantum Gravity}, year={2006}, volume={24}, pages={2565-2588} }

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 dynamics in the semiclassical limit, provided one incorrectly substitutes the non – Abelean group SU(2) by the Abelean group U(1) 3 in the calculations. The mere reason why that substitution was performed at all is that in the non – Abelean case the volume operator, pivotal for the definition of the…

## 68 Citations

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): 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…

Canonical Quantum Gravity, Constructive QFT, and Renormalisation

- PhysicsFrontiers in Physics
- 2020

The canonical approach to quantum gravity has been put on a firm mathematical foundation in the recent decades. Even the quantum dynamics can be rigorously defined, however, due to the tremendously…

Semiclassical analysis of the Loop Quantum Gravity volume operator. I. Flux Coherent States

- Mathematics
- 2008

We continue the semiclassical analysis of the Loop Quantum Gravity (LQG) volume operator that was started in the companion paper [23]. In the first paper we prepared the technical tools, in…

Algebraic Quantum Gravity (AQG). I. Conceptual Setup

- Physics
- 2007

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…

Semiclassical analysis of the Loop Quantum Gravity volume operator: Area Coherent States

- Mathematics
- 2009

We continue the semiclassical analysis of the Loop Quantum Gravity (LQG) volume operator that was started in the companion paper [23]. In the first paper we prepared the technical tools, in…

Cosmological coherent state expectation values in loop quantum gravity I. Isotropic kinematics

- PhysicsClassical and Quantum Gravity
- 2018

This is the first paper of a series dedicated to LQG coherent states and cosmology. The concept is based on the effective dynamics program of Loop Quantum Cosmology, where the classical dynamics…

Algebras of Quantum Variables for Loop Quantum Gravity, I. Overview

- Mathematics
- 2011

The operator algebraic framework plays an important role in mathematical physics. Many different operator algebras exist for example for a theory of quantum mechanics. In Loop Quantum Gravity only…

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…

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…

## References

SHOWING 1-10 OF 47 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…

Simplification of the spectral analysis of the volume operator in loop quantum gravity

- Physics
- 2004

The volume operator plays a crucial role in the definition of the quantum dynamics of loop quantum gravity (LQG). Efficient calculations for dynamical problems of LQG can therefore be performed only…

Algebraic Quantum Gravity (AQG). I. Conceptual Setup

- Physics
- 2007

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…

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…

Lectures on Loop Quantum Gravity

- Physics
- 2002

AbstractQuantum General Relativity (QGR), sometimes called Loop Quantum Gravity, has matured overthe past ﬁfteen years to a mathematically rigorous candidate quantum ﬁeld theory of the gravita-tional…

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…

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 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): 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…

QSD V : Quantum Gravity as the Natural Regulator of Matter Quantum Field Theories

- Physics
- 1997

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…