Related papers: The Loop Representation in Gauge Theories and Quan…
The conflict between the locality of general relativity, reflected in its space-time description, and the non-locality of quantum mechanics, contained in its Hilbert space description, is discussed. Gauge covariant non-local observables…
In the past, the possibility to employ (scalar) material reference systems in order to describe classical and quantum gravity directly in terms of gauge invariant (Dirac) observables has been emphasised frequently. This idea has been picked…
The problems which arise for a relativistic quantum mechanics are reviewed and critically examined in connection with the foundations of quantum field theory. The conflict between the quantum mechanical Hilbert space structure, the locality…
Research during the last decade demonstrates that effects originating on the Planck scale are currently being tested in multiple observational contexts. In this review we discuss quantum gravity phenomenological models and their possible…
We present a line by line derivation of canonical quantum mechanics stemming from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This viewpoint can…
In this paper canonical quantum gravity on noncommutative space-time is considered. The corresponding generalized classical theory is formulated by using the moyal star product, which enables the representation of the field quantities…
These notes are a didactic overview of the non perturbative and background independent approach to a quantum theory of gravity known as loop quantum gravity. The definition of real connection variables for general relativity, used as a…
General relativity successfully describes space-times at scales that we can observe and probe today, but it cannot be complete as a consequence of singularity theorems. For a long time there have been indications that quantum gravity will…
We review an attempt to set a suitable foundational principle for consistent quantization of gravity based on the canonical formulation. It requires extending the spacetime description of the relativistic postulates to also encompass an…
The equation of state for radiation is derived in a canonical formulation of the electromagnetic field. This allows one to include correction terms expected from canonical quantum gravity and to infer implications to the universe evolution…
We propose an approach which, by combining insights from Loop Quantum Gravity (LQG), Topos theory, Non-commutative Geometry \`a la Connes, and spacetime relationalism, provides fertile ground for the search of an adequate spacetime picture…
We give a very concise review of the group field theory formalism for non-perturbative quantum gravity, a higher dimensional generalisation of matrix models. We motivate it as a simplicial and local realisation of the idea of 3rd…
A brief review of various numerical techniques used in loop quantum cosmology and results is presented. These include the way extensive numerical simulations shed insights on the resolution of classical singularities, resulting in the key…
Loop quantum cosmology is an application of recent developments for a non-perturbative and background independent quantization of gravity to a cosmological setting. Characteristic properties of the quantization such as discreteness of…
A new kind of gauge theory is introduced, where the minimal coupling and corresponding covariant derivatives are defined in the space of functions pertaining to the functional Schroedinger picture of a given field theory. While, for…
We introduce a new loop expansion that provides a resolution of the identity in the Hilbert space of loop quantum gravity on a fixed graph. We work in the bosonic representation obtained by the canonical quantization of the spinorial…
Standard quantum mechanics and gravity are used to estimate the mass and size of idealized gravitating systems where position states of matter and geometry become indeterminate. It is proposed that well-known inconsistencies of standard…
We summarize recent developments at the interface of quantum gravity and quantum information, and discuss applications to the quantum geometry of space in loop quantum gravity. In particular, we describe the notions of link entanglement,…
Canonical quantum gravity provides insights into the quantum dynamics as well as quantum geometry of space-time by its implications for constraints. Loop quantum gravity in particular requires specific corrections due to its quantization…
Recent developments concerning canonical quantisation and gauge invariant quantum mechanical systems and quantum field theories are briefly discussed. On the one hand, it is shown how diffeomorphic covariant representations of the…