Related papers: The 2+1 Kepler Problem and Its Quantization
The two dimensional substructure of general relativity and gravity, and the two dimensional geometry of quantum effect by black hole are disclosed. Then the canonical quantization of the two dimensional theory of gravity is performed. It is…
In these notes we will review some approaches to 2+1 dimensional gravity and the way it is coupled to point-particles. First we look into some exact static and stationary solutions with and without cosmological constant. Next we study the…
General relativity becomes vastly simpler in three spacetime dimensions: all vacuum solutions have constant curvature, and the moduli space of solutions can be almost completely characterized. As a result, this lower dimensional setting…
We use the polygon representation of 2+1--dimensional gravity to explicitly carry out the canonical quantization of a universe with the topology of a torus. The mapping-class-invariant wave function for a quantum ''big bounce'', is…
It is argued that quantum gravity has an interpretation as a topological field theory provided a certain constraint from the path intergral measure is respected. The constraint forces us to couple gauge and matter fields to gravity for…
Taking the quantization of electromagnetism as the paradigm, we show how this procedure cannot work for Einstein gravity. However, it does work for conformal gravity, a fourth-order derivative, renormalizable theory of gravity that Bender…
We find that the momentum conjugate to the relative distance between two gravitating particles in their center of mass frame is a hyperbolic angle. This fact strongly suggests that momentum space should be taken to be a hyperboloid. We…
We consider the problem of (1+1)-dimensional quantum gravity coupled to particles. Working with the canonically reduced Hamiltonian, we obtain its post-Newtonian expansion for two identical particles. We quantize the (1+1)-dimensional…
The abstract quantum algebra of observables for 2+1 gravity is analysed in the limit of small cosmological constant. The algebra splits into two sets with an explicit phase space representation;~one set consists of $6g-6$ {\it commuting}…
It is well-known that the Einstein-Rosen solutions to the 3+1 dimensional vacuum Einstein's equations are in one to one correspondence with solutions of 2+1 dimensional general relativity coupled to axi-symmetric, zero rest mass scalar…
It is shown that if a metric in quantum gravity can be decomposed as a sum of classical and quantum parts then Einstein quantum gravity looks approximately like modified gravity with a nonminimal interaction between gravity and matter.
The phenomenon of quantum entanglement is thoroughly investigated, focussing especially on geometrical aspects and on bipartite systems. After introducing the formalism and discussing general aspects, some of the most important separability…
Chern-Simons formulation of the 2+1 dimensional Einstein gravity with negative cosmological constant is investigated when the spacetime has the topology ${\bf R}\times T^{2}$. The physical phase space is shown to be a direct product of two…
We investigate the behaviour of classical and quantum fields in the conical space-time associated with a point mass in 2+1 dimensions. We show that the presence of conical boundary conditions alters the electrostatic field of a point charge…
In certain scenarios of deformed relativistic symmetries relevant for non-commutative field theories particles exhibit a momentum space described by a non-abelian group manifold. Starting with a formulation of phase space for such particles…
We present a short, general and accessible introduction to quantizing gravity in the Heisenberg picture. We then apply this formalism to the scenario where two spatially superposed masses interact through the gravitational field. We discuss…
In this paper we review some aspects of relativistic particles' mechanics in the case of a non-trivial geometry of momentum space. We start with showing how the curved momentum space arises in the theory of gravity in 2+1 dimensions coupled…
Quantum gravity places entirely new challenges on the formulation of a consistent theory as well as on an extraction of potentially observable effects. Quantum corrections due to the gravitational field are commonly expected to be tiny…
In contrast to other approaches to (2+1)-dimensional quantum gravity, the Wheeler-DeWitt equation appears to be too complicated to solve explicitly, even for simple spacetime topologies. Nevertheless, it is possible to obtain a good deal of…
A 4-dimensional Lorentzian static space-time is equivalent to 3-dimensional Euclidean gravity coupled to a massless Klein-field. By canonically quantizing the coupling model in the framework of loop quantum gravity, we obtain a quantum…