Related papers: Classical Gravity on Fuzzy Space-Time
Noncommutative space has been found to be of use in a number of different contexts. In particular, one may use noncommutative spacetime to generate quantised gravity theories. Via an identification between the Moyal $\star$-product on…
Noncommutative geometry, in its many incarnations, appears at the crossroad of various researches in theoretical and mathematical physics: from models of quantum space-time (with or without breaking of Lorentz symmetry) to loop gravity and…
A specific theoretical framework is important for designing and conducting an experiment, and for interpretation of its results. The field of gravitational physics is expanding, and more clarity is needed. It appears that some popular…
The groupoid approach to noncommutative unification of general relativity with quantum mechanics is compared with the canonical gravity quantization. It is shown that by restricting the corresponding noncommutative algebra to its…
The correspondence between quantum mechanics and noncommutative geometry is illustrated in the context of the noncommutative ${\rm AdS}^2_{\theta}/{\rm CFT_1}$ duality where ${\rm CFT}_1$ is identified as conformal quantum mechanics. This…
We extend the non-commutative coordinates relationship into other than the Minkowski space-time. We clarify the non-commutativity dependency to the geometrical structure. As well as, we find an inverse map between Riemann's normal and…
These notes comprise the first of two articles devoted to the construction of exact solutions of noncommutative gauge theory in two spacetime dimensions. This first part deals solely with the classical theory on a noncommutative torus.…
The conventional phase space of classical physics treats space and time differently, and this difference carries over to field theories and quantum mechanics (QM). In this paper, the phase space is enhanced through two main extensions.…
Geometric structure of spherically-symmetric space-time in metric-affine gauge theory of gravity is studied. Restrictions on curvature tensor and Bianchi identities are obtained. By using certain simple gravitational Lagrangian the solution…
We discuss various descriptions of a quantum particle on noncommutative space in a (possibly non-constant) magnetic field. We have tried to present the basic facts in a unified and synthetic manner, and to clarify the relationship between…
A new noncommutative spacetime of structure $ {\cal M}^4 \times Z_2 \times Z_2$ is proposed. The generalized Hilbert-Einstein action contains gravity, all known interactions and Higgs field. This theory can also provide a unified geometric…
Within the gauge-theoretic approach of gravity, the gauging of an enlarged symmetry of the tangent space in four dimensions allows gravity to be unified with internal interactions. We study the unification of the Conformal and…
We generalize the Hamiltonian picture of General Relativity coupled to classical matter, known as geometrodynamics, to the case where such matter is described by a Quantum Field Theory in Curved Spacetime, but gravity is still described by…
It is shown that a unified description of classical and `quantum mechanical' gravity in its linearized form is possible.
We consider a hypothesis in which classical space-time emerges from information exchange (interactions) between quantum fluctuations in the gravity theory. In this picture, a line element would arise as a statistical average of how…
The authors introduced in a previous paper the notion of fuzzy Gromov-Hausdorff distance between non-Archimedean compact fuzzy metric spaces, presenting a fuzzy version of the Gromov's completeness theorem. In this paper we present a fuzzy…
We show that under certain boundary conditions on the matter fields and on the fluctuations of the background metric the gravity-matter system can be coupled to the boundary of space-time through the stress-energy tensor. The connection of…
It is well known that in quantum gravity, the very geometry of space and time is subject to continual fluctuation. The mathematical formulation for this old theory is still lacking. This article formulates this more than forty-year-old…
A reconciliation of gravitation and electromagnetism has eluded physics for neearly a century. It is argued here that this is because both quantum physics and classical physics are set in differentiable space time manifolds with point…
The implications of restricting the covariance principle within a Gaussian gauge are developed both on a classical and a quantum level. Hence, we investigate the cosmological issues of the obtained Schr\"odinger Quantum Gravity with respect…