Related papers: Classical Gravity on Fuzzy Space-Time
Trajectories in the space of the unitarily inequivalent representations of the canonical commutation relations are shown to be classical trajectories. Under convenient conditions, they may exhibit properties typical of chaotic behavior in…
The gauge connections corresponding to electromagnetism, Yang-Mills theory and Einstein gravity can be derived by assuming specific commutation relations between the phase-space variables of a first quantized theory. Extending the procedure…
We present an overview of recent developments concerning modifications of the geometry of space-time to describe various physical processes of interactions among classical and quantum configurations. We concentrate in two main lines of…
Noncommutativity of the spacetime coordinates has been explored in several contexts, mostly associated to phenomena at the Planck length scale. However, approaching this question through deformation theory and the principle of stability of…
I review and discuss some recent developments in non-perturbative approaches to quantum gravity, with an emphasis on discrete formulations, and those coming from a classical connection description.
We consider the quasi-commutative approximation to a noncommutative geometry defined as a generalization of the moving frame formalism. The relation which exists between noncommutativity and geometry is used to study the properties of the…
We propose an approach which, by combining insights from Loop Quantum Gravity (LQG), Topos theory, Non-commutative Geometry \`a la Connes, and spacetime relationalism, provides fertile ground for the search of an adequate spacetime picture…
We consider the possibility of energy being exchanged between the scalar and matter fields in scalar-tensor theories of gravity. Such an exchange provides a new mechanism which can drive variations in the gravitational 'constant' G. We find…
A new direction to understand gravity has recently been explored by considering classical gravity to be a derived interaction from an underlying theory. This underlying theory would involve new degrees of freedom at a deeper level and it…
Questioning the experimental basis of continuous descriptions of fundamental interactions we discuss classical gravity as an effective continuous first-order approximation of a discrete interaction. The sub-dominant contributions produce a…
We review aspects of loop quantum gravity in a pedagogical manner, with the aim of enabling a precise but critical assessment of its achievements so far. We emphasise that the off-shell (`strong') closure of the constraint algebra is a…
We discuss the possibility that spacetime geometry may be an emergent phenomenon. This idea has been motivated by the Analogue Gravity programme. These are systems where the kinematics of small perturbations are dominated by an effective…
We consider both the co-ordinates and momenta to be non-commutative and define a non-commutative version of Lorentz symmetry which has a smooth limit to the standard Lorentz symmetry. The Poincar\acute{e} algebra in this spacetime has also…
We present a unification scenario of the conformal and fuzzy gravities with the internal interactions, based on the observation that the tangent space of a curved space and the space itself do not necessarily have the same dimensions.…
Non commutative geometry is creating new possibilities for physics. Quantum spacetime geometry and post inflationary models of the universe with matter creation have an enormous range of scales of time, distance and energy in between. There…
Classical gravitation theory is formulated as gauge theory on natural bundles where gauge symmetries are general covariant transformations and a gravitational field is a Higgs field responsible for their spontaneous symmetry breaking.
Mimetic gravity is a modified theory of gravity which is able to incorporate dark matter into the underlying geometry of space-time by isolating the conformal degree of freedom. The theory has been studied extensively in the cosmological…
We conjecture that the modified commutation relations suggested in the context of quantum gravity (QG) persist also in the classical limit, if the momentum of the classical object is not too large, and calculate the corresponding perihelion…
We present the formalism for the covariant treatment of gravitational radiation in a magnetized environment and discuss the implications of the field for gravity waves in the cosmological context. Our geometrical approach brings to the fore…
While Quantum Gravity remains elusive and Quantum Field Theory retains the interpretational difficulties of Quantum Mechanics, we have introduced an alternate approach to the unification of particles, fields, space and time, suggesting that…