525 citations · 7.1k across the 109 of their papers we have counts for
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Quantum gravity in the triangular gauge
Thomas Thiemann
Vielbeins are necessary when coupling General Relativity (GR) to fermionic matter. This enhances the gauge group of GR to include local Lorentz transformations. In view of a reduce…
Hamiltonian Theory: Dynamics
Thomas Thiemann, Kristina Giesel
This chapter focuses on the status of the implementation of the dynamics in the canonical version of Loop Quantum Gravity (LQG). Concretely this means to provide a mathematical mea…
Exact quantisation of U(1) quantum gravity via exponentiation of the hypersurface deformation algebroid
T. Thiemann
The U(1) model for 3+1 Euclidian signature general relativity is an interacting, generally covariant field theory with two physical polarisations that shares many features of L…
Non-degenerate metrics, hypersurface deformation algebra, non-anomalous representations and density weights in quantum gravity
T. Thiemann
A basic assumption in classical GR is that the metric field is nowhere degenerate in spacetime. In particular the induced metric on Cauchy surfaces must be nowhere degenerate. It i…
Hamiltonian renormalisation VI: Parametrised field theory on the cylinder
T. Thiemann, E. -A. Zwicknagel
Hamiltonian Renormalisation, as defined within this series of works, was derived from covariant Wilson renormalisation via Osterwalder-Schrader reconstruction. As such it directly…
On propagation in Loop Quantum Gravity
Thomas Thiemann, Madhavan Varadarajan
A rigorous implementation of the Wheeler-Dewitt equations was derived in the context of Loop Quantum Gravity (LQG) and was coined Quantum Spin Dynamics (QSD). The Hamiltonian const…
Backreaction in Cosmology
S. Schander, T. Thiemann
In this review, we investigate the question of backreaction in different approaches to cosmological perturbation theory, and with a special focus on quantum theoretical aspects. By…
Asymptotically flat boundary conditions for the model for Euclidean Quantum Gravity
Sepideh Bakhoda, Hossein Shojaie, Thomas Thiemann
A generally covariant gauge theory describing the limit of Euclidean general relativity is an interesting test laboratory for general relativity, specially bec…
Canonical Quantum Gravity, Constructive QFT and Renormalisation
Thomas Thiemann
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…
Hamiltonian Renormalisation V: Free Vector Bosons
Klaus Liegener, Thomas Thiemann
In a recent proposal we applied methods from constructive QFT to derive a Hamiltonian Renormalisation Group in order to employ it ultimately for canonical quantum gravity. The prop…
Quantum Cosmological Backreactions IV: Constrained Quantum Cosmological Perturbation Theory
S. Schander, T. Thiemann
This is the fourth paper in a series of four in which we use space adiabatic methods in order to incorporate backreactions among the homogeneous and between the homogeneous and inh…
Hamiltonian diagonalization in hybrid quantum cosmology
Beatriz Elizaga Navascués, Guillermo A. Mena Marugán, Thomas Thiemann
We explore the possibility of selecting a natural vacuum state for scalar and tensor gauge-invariant cosmological perturbations in the context of hybrid quantum cosmology, by ident…
Hamiltonian Renormalisation II. Renormalisation Flow of 1+1 dimensional free scalar fields: Derivation
Thorsten Lang, Klaus Liegener, Thomas Thiemann
In the companion paper we motivated a renormalisation flow on Osterwalder-Schrader data (OS-data) consisting of 1. a Hilbert space, 2. a cyclic vacuum and 3. a Hamiltonian annihila…
Hamiltonian Renormalisation IV. Renormalisation Flow of D+1 dimensional free scalar fields and Rotation Invariance
Thorsten Lang, Klaus Liegener, Thomas Thiemann
In this article we extend the test of Hamiltonian Renormalisation proposed in this series of articles to the D-dimensional case using a massive free scalar field. The concepts we i…
Hamiltonian Renormalization III. Renormalisation Flow of 1+1 dimensional free scalar fields: Properties
Thorsten Lang, Klaus Liegener, Thomas Thiemann
This is the third paper in a series of four in which a renormalisation flow is introduced which acts directly on the Osterwalder-Schrader data (OS data) without recourse to a path…
Hamiltonian Renormalisation I: Derivation from Osterwalder-Schrader Reconstruction
Thorsten Lang, Klaus Liegener, Thomas Thiemann
A possible avenue towards a non-perturbative Quantum Field Theory (QFT) on Minkowski space is the constructive approach which employs the Euclidian path integral formulation, in th…
Uniqueness of the Representation in Homogeneous Isotropic LQC
Jonathan Engle, Maximilian Hanusch, Thomas Thiemann
We show that the standard representation of homogeneous isotropic loop quantum cosmology (LQC) is the GNS-representation that corresponds to the unique state on the reduced quantum…
Towards the fundamental spectrum of the Quantum Yang-Mills Theory
Klaus Liegener, Thomas Thiemann
In this work we focus on the quantum Einstein-Yang-Mills sector quantised by the methods of Loop Quantum Gravity (LQG). We point out the improved UV behaviour of the coupled system…
Projective Limits of State Spaces IV. Fractal Label Sets
Suzanne Lanéry, Thomas Thiemann
Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski [Kijowski 1977] to represent quantum states as project…
Projective Loop Quantum Gravity II. Searching for Semi-Classical States
Suzanne Lanéry, Thomas Thiemann
In [arXiv:1411.3592] an extension of the Ashtekar-Lewandowski (AL) state space of Loop Quantum Gravity was set up with the help a projective formalism introduced by Kijowski [Kijow…
Stable coherent states
Antonia Zipfel, Thomas Thiemann
We analyze the stability under time evolution of complexifier coherent states (CCS) in one-dimensional mechanical systems. A system of coherent states is called stable if it evolve…
Projective Loop Quantum Gravity I. State Space
Suzanne Lanéry, Thomas Thiemann
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 d…
Projective Limits of State Spaces III. Toy-Models
Suzanne Lanéry, Thomas Thiemann
In this series of papers, we investigate the projective framework initiated by Jerzy Kijowski and Andrzej Okołów, which describes the states of a quantum theory as projective famil…
Projective Limits of State Spaces II. Quantum Formalism
Suzanne Lanéry, Thomas Thiemann
In this series of papers, we investigate the projective framework initiated by Jerzy Kijowski and Andrzej Okołów, which describes the states of a quantum theory as projective famil…