Related papers: Extended diffeomorphism algebras in (quantum) grav…
The study of general two dimensional models of gravity allows to tackle basic questions of quantum gravity, bypassing important technical complications which make the treatment in higher dimensions difficult. As the physically important…
After a brief chronological sketch of developments in non-perturbative canonical quantum gravity, some of the recent mathematical results are reviewed. These include: i) an explicit construction of the quantum counterpart of Wheeler's…
A deformation of the algebra of diffeomorphisms is constructed for canonically deformed spaces with constant deformation parameter theta. The algebraic relations remain the same, whereas the comultiplication rule (Leibniz rule) is different…
We describe a completely general and fully non-perturbative framework for constructing dynamical reference frames in generally covariant theories, and for understanding the gauge-invariant observables that they yield. Our approach makes use…
We discuss in a critical way the physical foundations of geometric structure of relativistic theories of gravity by the so-called Ehlers-Pirani-Schild formalism. This approach provides a natural interpretation of the observables showing how…
We postulate that the fundamental principles of Quantum Gravity are diffeomorphism symmetry, unitarity, and locality. Local observables are compatible with diffeomorphism symmetry in the presence of diff anomalies, which modify the symmetry…
The algebra of diffeomorphisms derived from general coordinate transformations on commuting coordinates is represented by differential operators on noncommutative spaces. The algebra remains unchanged, the comultiplication however is…
We present how the formalism of geometric phases in adiabatic quantum dynamics provides geometric realisations permitting to ``embody'' the Everett's many-worlds interpretation of quantum mechanics, including interferences between the…
A simple mathematical extension of quantum theory is presented. As well as opening the possibility of alternative methods of calculation, the additional formalism implies a new physical interpretation of the standard theory by providing a…
Relevant algebraic structures for the description of Quantum Mechanics in the Heisenberg picture are replaced by tensorfields on the space of states. This replacement introduces a differential geometric point of view which allows for a…
Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…
We show that the Dirac equation can be rewritten as a relation describing the fundamental symmetry group of special topological manifold corresponding to the Dirac wave field. It leads to unification of the time-space and internal…
This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that…
A first attempt at adding matter degrees of freedom to the two-dimensional ``vacuum'' gravity model presented in gr-qc/9907071 is analyzed in this paper. Just as in the previous pure gravity case, quantum diffeomorphism operators…
If the diffeomorphism symmetry of general relativity is fully implemented into a path integral quantum theory, the path integral leads to a partition function which is an invariant of smooth manifolds. We comment on the physical…
We provide a new formulation of nonrelativistic diffeomorphism invariance. It is generated by localising the usual global Galilean Symmetry. The correspondence with the type of diffeomorphism invariant models currently in vogue in the…
The formalism of quantum state space geometry on manifolds of generalised coherent states is proposed as a natural setting for the construction of geometric dual descriptions of non-relativistic quantum systems. These state manifolds are…
First-order general relativity in $n$ dimensions ($n \geq 3$) has an internal gauge symmetry that is the higher-dimensional generalization of three-dimensional local translations. We report the extension of this symmetry for $n$-dimensional…
We present an extended version of Riemannian geometry suitable for the description of current formulations of double field theory (DFT). This framework is based on graded manifolds and it yields extended notions of symmetries, dynamical…
This series of lectures gives a simple and self-contained introduction to the non-perturbative and background independent loop approach of canonical quantum gravity. The Hilbert space of kinematical quantum states is constructed and a…