Related papers: Quantum gravity and non-commutative spacetimes in …
We apply a recent proposal for defining states and observables in quantum gravity to simple models. First, we consider a Klein-Gordon particle in an ex- ternal potential in Minkowski space and compare our proposal to the theory ob- tained…
We apply Lie algebra deformation theory to the problem of identifying the stable form of the quantum relativistic kinematical algebra. As a warm up, given Galileo's conception of spacetime as input, some modest computer code we wrote zeroes…
We give an explicitly gauge invariant canonical analysis of linearized quadratic gravity theories in three dimensions for both flat and de-Sitter backgrounds. In flat backgrounds, we also study the effects of gravitational Chern-Simons…
We recall a classical theory of torsion gravity with an asymmetric metric, sourced by a Nambu-Goto + Kalb-Ramond string . We explain why this is a significant gravitational theory, and in what sense classical general relativity is an…
This paper is a serious attempt at reconciling quantum and classical mechanics through the concept of dynamic space and the acceptance of non-zero Ricci tensor for vacuum. Starting with scalar particles, the paper shows that with those two…
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…
Different approaches are compared to formulation of quantum mechanics of a particle on the curved spaces. At first, the canonical, quasi-classical and path integration formalisms are considered for quantization of geodesic motion on the…
The focus of this PhD thesis is on applications, new developments and extensions of the noncommutative gravity theory proposed by Julius Wess and his group. In part one we propose an extension of the usual symmetry reduction procedure to…
We will highlight that despite there being various approaches to quantum gravity, there are universal approach-independent features of quantum gravity. The geometry of spacetime becomes an emergent structure, which emerges from some purely…
A new canonical Hopf algebra called the quantum pseudo-K\"ahler plane is introduced. This quantum group can be viewed as a deformation quantization of the complex two-dimensional plane $\mathbb{C}^2$ with a pseudo-K\"ahler metric, or as a…
In quantum field theory the creation and annihilation operators that are located at the points in 3-momentum space have commutation relations that are conserved under the action of a $U({\infty})$ group. Here it is shown how to define an…
We investigate several problems in relativity and particle physics where symmetries play a central role; in all cases geometric properties of Lie groups and their quotients are related to physical effects. The first part is concerned with…
Canonical methods allow the derivation of effective gravitational actions from the behavior of space-time deformations reflecting general covariance. With quantum effects, the deformations and correspondingly the effective actions change,…
Quantum gravity (or quantum spacetime) is to unify general relativity and quantum mechanics into a single theoretical framework and presented as the most important open puzzle in fundamental physics. The development of a microscopic theory…
Loop Quantum Gravity heavily relies on a connection formulation of General Relativity such that 1. the connection Poisson commutes with itself and 2. the corresponding gauge group is compact. This can be achieved starting from the Palatini…
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…
A major unsolved problem in theoretical physics is to reconcile the classical theory of general relativity with quantum mechanics. These lectures will deal with an attempt to describe quantum gravity as a path integral over geometries known…
A reformulation of the Wheeler-DeWitt equation which highlights the role of gauge-invariant three-geometry elements is presented. It is noted that the classical super-Hamiltonian of four-dimensional gravity as simplified by Ashtekar through…
We present the generalisation to (3+1) dimensions of a quantum deformation of the (2+1) (Anti)-de Sitter and Poincar\'e Lie algebras that is compatible with the conditions imposed by the Chern-Simons formulation of (2+1) gravity. Since such…
The third modification of the space-time geometry is considered. (The first modification is the spacial relativity, the second one is the general relativity.) After the third modification of the space-time geometry the motion of free…