Related papers: Noncommutative Quantum Gravity
General relativity under the assumption of noncommuting components of the tetrad field is considered in this paper. Since the algebraic properties of the tetrad field representing the gravitational field are assumed to correspond to the…
In recent years, many new developments in theoretical physics, and in practical applications rely on different techniques of noncommutative algebras. In this review, we introduce the basic concepts and techniques of noncommutative physics…
We present a self-contained and consistent formulation of noncommutative (NC) gauge theory of gravity, focusing on spherically symmetric black hole geometries. Our construction starts from the gauge-theoretic viewpoint of Poincar\'{e} (or…
In this paper, we establish and employ a local framework to the first order of Riemann's curvature tensor in order to develop the corresponding coordinate non commutativity into general manifolds. We also exploit a new translation of…
Various approaches by the author and collaborators to define gravitational fluctuations associated with a noncommutative space are reviewed.
The algebras of non-relativistic and of classical mechanics are unstable algebraic structures. Their deformation towards stable structures leads, respectively, to relativity and to quantum mechanics. Likewise, the combined relativistic…
The symplectic geometry of the phase space associated with a charged particle is determined by the addition of the Faraday 2-form to the standard structure on the Euclidean phase space. In this paper we describe the corresponding algebra of…
In this survey article we discuss a framework of noncommutative geometry with differential graded categories as models for spaces. We outline a construction of the category of noncommutative spaces and also include a discussion on…
The existing approaches to quantization of gravity aim at giving quantum description of 3-geometry following to the ideas of the Wheeler -- DeWitt geometrodynamics. In this description the role of gauge gravitational degrees of freedom is…
There ought to exist a reformulation of quantum mechanics which does not refer to an external classical spacetime manifold. Such a reformulation can be achieved using the language of noncommutative differential geometry. A consequence which…
In a recent paper we have suggested that a formulation of quantum mechanics should exist, which does not require the concept of time, and that the appropriate mathematical language for such a formulation is noncommutative differential…
We reconsider a gauge theory of gravity in which the gauge group is the conformal group SO(4,2) and the action is of the Yang-Mills form, quadratic in the curvature. The resulting gravitational theory exhibits local conformal symmetry and…
A key problem in the attempt to quantize the gravitational field is the choice of boundary conditions. These are mixed, in that spatial and normal components of metric perturbations obey different sets of boundary conditions. In the…
The Covariant Canonical Gauge theory of Gravity is generalized by including at the Lagrangian level all possible quadratic curvature invariants. In this approach, the covariant Hamiltonian principle and the canonical transformation…
We consider a model of Quantum Gravity phenomenology, based on the idea that space-time may have some unknown granular structure that respects the Lorentz symmetry. The proposal involves non-trivial couplings of curvature to matter fields…
In this paper we discuss on the phenomenological footprints of gauge invariant theories of gravity where the gravitational effects are due not only to spacetime curvature, but also to vectorial nonmetricity. We explore the possibility that…
We propose that the consistent field renormalization of gravity requires a specific Weyl transformation of the metric tensor. As a consequence, proper length and time, as well as energy and momentum, become functions of scale. We estimate…
We argue that a field theory defined on noncommutative (NC) spacetime should be regarded as a theory of gravity, which we refer to as the emergent gravity. A whole point of the emergent gravity is essentially originated from the basic…
We have constructed a non-relativistic theory of quantum mechanics based on local modulus symmetry. The resulting connection in the covariant derivative is identified as the escape velocity of the gravitational field. A new real and…
Close to the Planck energy scale, the quantum nature of space-time reveals itself and all forces, including gravity, should be unified so that all interactions correspond to just one underlying symmetry. In the absence of a full quantum…