# Towards the QFT on curved spacetime limit of QGR: II. A concrete implementation

@article{Sahlmann2002TowardsTQ, title={Towards the QFT on curved spacetime limit of QGR: II. A concrete implementation}, author={H. Sahlmann and Thomas Thiemann}, journal={Classical and Quantum Gravity}, year={2002}, volume={23}, pages={909 - 954} }

The present paper is the companion of Sahlmann and Thiemann (2006 Towards the QFT on curved spacetime limit of QGR: I. A general scheme Class. Quantum Grav. 23 867) in which we proposed a scheme that tries to derive the quantum field theory (QFT) on curved spacetimes (CST) limit from background-independent quantum general relativity (QGR). The constructions of the companion paper make heavy use of the notion of semiclassical states for QGR. In the present paper, we employ the complexifier…

## Figures from this paper

## 130 Citations

Towards the QFT on curved spacetime limit of QGR: I. A general scheme

- Physics
- 2002

In this paper and the companion paper (Sahlmann and Thiemann 2006 Towards the QFT on curved spacetime limit of QGR: II. A concrete implementation Class. Quantum Grav. 23 909), we address the question…

Towards loop quantum supergravity (LQSG): II. p-form sector

- Physics
- 2013

In our companion paper, we focused on the quantization of the Rarita–Schwinger sector of supergravity theories in various dimensions by using an extension of loop quantum gravity to all spacetime…

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…

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 loop quantum gravity (LQG) coherent states and cosmology. The concept is based on the effective dynamics program of Loop Quantum Cosmology, where the…

On the Low-Energy Ramifications and a Mathematical Extension of Loop Quantum Gravity

- Mathematics, Physics
- 2004

In this thesis we address two remaining open questions in loop quantum gravity. The first deals with the low-energy limit of the theory. We illustrate some of the conceptual difficulties and their…

New variables for classical and quantum gravity in all dimensions: IV. Matter coupling

- Physics
- 2013

We employ the techniques introduced in the companion papers (Bodendorfer et al 2011 arXiv:1105.3703 [gr-qc]; arXiv:1105.3704 [gr-qc]; arXiv:1105.3705 [gr-qc]) to derive a connection formulation of…

On (cosmological) singularity avoidance in loop quantum gravity

- Mathematics
- 2006

Loop quantum cosmology (LQC), mainly due to Bojowald, is not the cosmological sector of loop quantum gravity (LQG). Rather, LQC consists of a truncation of the phase space of classical general…

Born--Oppenheimer decomposition for quantum fields on quantum spacetimes

- Physics
- 2009

Quantum Field Theory on Curved Spacetime (QFT on CS) is a well established theoretical framework which intuitively should be a an extremely effective description of the quantum nature of matter when…

Coherent states, quantum gravity and the Born-Oppenheimer approximation, I: General considerations

- Physics
- 2015

This article, as the first of three, aims at establishing the (time-dependent) Born-Oppenheimer approximation, in the sense of space adiabatic perturbation theory, for quantum systems constructed by…

Analysing (cosmological) singularity avoidance in loop quantum gravity using U$(1)^3$ coherent states and Kummer's functions

- Mathematics
- 2021

Using a new procedure based on Kummer’s Confluent Hypergeometric Functions, we investigate the question of singularity avoidance in loop quantum gravity (LQG) in the context of U(1) complexifier…

## References

SHOWING 1-10 OF 57 REFERENCES

Towards the QFT on curved spacetime limit of QGR: I. A general scheme

- Physics
- 2002

In this paper and the companion paper (Sahlmann and Thiemann 2006 Towards the QFT on curved spacetime limit of QGR: II. A concrete implementation Class. Quantum Grav. 23 909), we address the question…

Loop Quantum Gravity

- PhysicsLiving reviews in relativity
- 1998

A general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity is provided, and a guide to the relevant literature is provided.

Complexifier coherent states for quantum general relativity

- Mathematics
- 2002

Recently, substantial amount of activity in quantum general relativity (QGR) has focused on the semiclassical analysis of the theory. In this paper, we want to comment on two such developments: (1)…

Gauge field theory coherent states (GCS): II. Peakedness properties

- Mathematics
- 2001

In this article we apply the methods outlined in the previous paper of this series to the particular set of states obtained by choosing the complexifier to be a Laplace operator for each edge of a…

Introduction to Modern Canonical Quantum General Relativity

- Physics
- 2001

This is an introduction to the by now fifteen years old research field of canonical quantum general relativity, sometimes called "loop quantum gravity". The term "modern" in the title refers to the…

Gauge field theory coherent states (GCS): III. Ehrenfest theorems

- Mathematics
- 2001

In the preceding paper of this series of articles we established peakedness properties of a family of coherent states that were introduced by Hall for any compact gauge group and were later…

Gauge Field Theory Coherent States (GCS) : III.

- Mathematics
- 2000

In the preceding paper of this series of articles we established peakedness properties of a family of coherent states that were introduced by Hall for any compact gauge group and were later…

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…

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.…

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…