Related papers: Combinatorial space from loop quantum gravity
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…
A new approach to a unified theory of quantum gravity based on noncommutative geometry and canonical quantum gravity is presented. The approach is built around a *-algebra generated by local holonomy-diffeomorphisms on a 3-manifold and a…
We consider the background-independent quantization of a general scale-invariant theory of gravity with matter, which supports a conserved Weyl current recently suggested as a natural flow of time. For scalar-metric systems, a conformal…
In this work we introduce a criterion for testing general covariance in effective quantum gravity theories. It adapts the analysis of invariance under general spacetime diffeomorphisms of the Einstein-Hilbert action to the case of effective…
Two gauge and diffeomorphism invariant theories on the Yang-Mills phase space are studied. They are based on the Lie-algebras $so(1,3)$ and $\widetilde{so(3)}$ -- the loop-algebra of $so(3)$. Although the theories are manifestly real, they…
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…
We investigate the construction of coherent states for quantum theories of connections based on graphs embedded in a spatial manifold, as in loop quantum gravity. We discuss the many subtleties of the construction, mainly related to the…
General Relativity is usually formulated as a theory with gauge invariance under the diffeomorphism group, but there is a 'dilaton' formulation where it is in addition invariant under Weyl transformations, and a 'unimodular' formulation…
Spherically symmetric models of loop quantum gravity have been studied recently by different methods that aim to deal with structure functions in the usual constraint algebra of gravitational systems. As noticed by Gambini and Pullin, a…
Conceptual difficulties in semiclassical and quantum gravity arise from diffeomorphism invariance of classical general relativity. With a motivation to shed some light on these difficulties, we study a class of toy models for which…
A generalized quantization principle is considered, which incorporates nontrivial commutation relations of the components of the variables of the quantized theory with the components of the corresponding canonical conjugated momenta…
It is shown that introducing the quantum effects using deBroglie--Bohm theory in the canonical formulation of gravity would change the constraints algebra. The new algebra is derived and shown that it is the clear projection of general…
Building on a recent proposal for a quantum reduction to spherical symmetry from full loop quantum gravity, we investigate the relation between a quantisation of spherically symmetric general relativity and a reduction at the quantum level.…
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 covariance of loop quantum gravity studies of spherically symmetric space-times has recently been questioned. This is a reasonable worry, given that they are formulated in terms of slicing-dependent variables. We show explicitly that…
We demonstrate the existence of spinorial states in a theory of canonical quantum gravity without matter. This should be regarded as evidence towards the conjecture that bound states with particle properties appear in association with…
We discuss the BRST cohomologies of the invariants associated with the description of classical and quantum gravity in four dimensions, using the Ashtekar variables. These invariants are constructed from several BRST cohomology sequences.…
The conventional group of four-dimensional diffeomorphisms is not realizeable as a canonical transformation group in phase space. Yet there is a larger field-dependent symmetry transformation group which does faithfully reproduce 4-D…
The notion of a measure on the space of connections modulo gauge transformations that is invariant under diffeomorphisms of the base manifold is important in a variety of contexts in mathematical physics and topology. At the formal level,…
We show that representations of the group of spacetime diffeomorphism and the Dirac algebra both arise in a phase-space histories version of canonical general relativity. This is the general-relativistic analogue of the novel time structure…