Related papers: Canonical Quantum Supergravity in Three Dimensions…
We develop a semiclassical theory of modified gravity with nontrivial spacetime torsion. In particular, we show that the semiclassical treatment can be axiomatized in the case of Einstein--Cartan theory with a nonminimally coupled, free…
The correct implementation of the Loop Quantum Gravity to the early homogeneous Universe has been the subject of a long debate in the literature because the SU(2) symmetry cannot be properly retained. The role of this symmetry is expressed…
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…
For general off-shell N=2 supergravity-matter systems in three spacetime dimensions, a formalism is developed to reduce the corresponding actions from superspace to components. The component actions are explicitly computed in the cases of…
Canonical quantization is often used to suggest new effects in quantum gravity, in the dynamics as well as the structure of space-time. Usually, possible phenomena are first seen in a modified version of the classical dynamics, for instance…
Hamiltonian constraints feature in the canonical formulation of general relativity. Unlike typical constraints they cannot be associated with a reduction procedure leading to a non-trivial reduced phase space and this means the physical…
These lectures briefly review our current understanding of classical and quantum gravity in three spacetime dimensions, concentrating on the quantum mechanics of closed universes and the (2+1)-dimensional black hole. Three formulations of…
The canonical approach to Riemannian quantum gravity is reviewed with reference to local supersymmetry, to the classical boundary-value problem arising from the Hartle-Hawking quantum state, and particularly for (anti-)self-dual geometries.…
To clarify some issues raised by D'Eath's recent proposal for the physical states of $N=1$ supergravity in four dimensions, we study pure (topological) $N=2$ supergravity in three dimensions, which is formally very similar, but much easier…
Supergravity theory in $2+\epsilon$ dimensions is studied. It is invariant under supertransformations in 2 and 3 dimensions. One-loop divergence is explicitly computed in the background field method and a nontrivial fixed point is found. In…
We extensively study the ultraviolet quantum properties of a nonlocal action for gravity nonminimally coupled to matter. The theory unifies matter and gravity in an action principle such that all the classical solutions of Einstein's theory…
In this paper we investigate possible consistent ghost-free models containing massive spin 2 particles in three dimensions. We work in a constructive approach based on the frame-like gauge invariant description for such massive spin 2…
The locally supersymmetric extension of the most general gravity theory in three dimensions leading to first order field equations for the vielbein and the spin connection is constructed. Apart from the Einstein-Hilbert term with…
We discuss the quantization of theories which are formulated using compensating fields. In particular, we discuss the relation between the components formulation and the superspace formulation of supergravity theories. The requirement that…
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 the tremendously non-polynomial character of the…
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…
Dirac's approach to the canonical quantization of constrained systems is applied to $N = 1$ supergravity, with or without gauged supermatter. Two alternative types of boundary condition applicable to quantum field theory or quantum gravity…
Starting from an action for discretized gravity we derive a canonical formalism that exactly reproduces the dynamics and (broken) symmetries of the covariant formalism. For linearized Regge calculus on a flat background -- which exhibits…
A semifinite spectral triple for an algebra canonically associated to canonical quantum gravity is constructed. The algebra is generated by based loops in a triangulation and its barycentric subdivisions. The underlying space can be seen as…
We compare different treatments of the constraints in canonical quantum gravity. The standard approach on the superspace of 3--geometries treats the constraints as the sole carriers of the dynamic content of the theory, thus rendering the…