相关论文: On a covariant version of Caianiello's Model

We show that tensoriality constraints in noncommutative Riemannian geometry in the 2-dimensional bicrossproduct model quantum spacetime algebra [x,t]=\lambda x drastically reduce the moduli of possible metrics g up to normalisation to a…

This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at "quantum…

We propose a new method to define theories of random geometries, using an explicit and simple map between metrics and large hermitian matrices. We outline some of the many possible applications of the formalism. For example, a…

We provide geometric quantization of the vertical cotangent bundle V^*Q equipped with the canonical Poisson structure. This is a momentum phase space of non-relativistic mechanics with the configuration bundle Q -> R. The goal is the…

The canonical analysis and subsequent quantization of the (2+1)-dimensional action of pure gravity plus a cosmological constant term is considered, under the assumption of the existence of one spacelike Killing vector field. The proper…

The basic framework for a systematic construction of a quantum theory of Riemannian geometry was introduced recently. The quantum versions of Riemannian structures --such as triad and area operators-- exhibit a non-commutativity. At first…

Models of gravitational collapse provide important means to test whether non-classical space-time effects motivated for instance by quantum gravity can be realized in generic ways in physically relevant situations. Here, a detailed analysis…

A covariant reformulation of General Relativity is briefly considered from three points of view: geometrodynamics, Lagrange-Euler field theory, and gauge field theory. From a geometrodynamics perspective, a definition of the reference frame…

We briefly report our application of a version of noncommutative geometry to the quantum Euclidean space $R^N_q$, for any $N \ge 3$; this space is covariant under the action of the quantum group $SO_q(N)$, and two covariant differential…

One of the main technical obstacles in constructing a consistent theory of quantum gravity is that the metric itself defines the causal structure required for quantization. This motivates implementing quantum aspects of gravity through an…

An earlier proposed theory with linear-gonihedhic action for quantum gravity is reviewed. One can consider this theory as a "square root" of classical gravity with a new fundamental constant of dimension one. We demonstrate also, that the…

A new approach to quantum gravity is presented based on a nonlinear quantization scheme for canonical field theories with an implicitly defined Hamiltonian. The constant mean curvature foliation is employed to eliminate the momentum…

The motion of a quantum particle constrained to a two-dimensional non-compact Riemannian manifold with non-trivial metric can be described by a flat-space Schroedinger-type equation at the cost of introducing local mass and metric and…

Various extensions to Riemann geometry have been proposed since the inception of general relativity (GR). The aim has been and continues to be to construct a quantum and dynamic spacetime that incorporates the well-known classical (static)…

The gauge symmetry of classical general relativity under space-time diffeomorphisms implies that any path integral quantization which can be interpreted as a sum over space-time geometries, gives rise to a formal invariant of smooth…

A well-defined regularized path integral for Lorentzian quantum gravity in three and four dimensions is constructed, given in terms of a sum over dynamically triangulated causal space-times. Each Lorentzian geometry and its associated…

The problem of constructing a quantum theory of gravity has been tackled with very different strategies, most of which relying on the interplay between ideas from physics and from advanced mathematics. On the mathematical side, a central…

We study general relativity in the framework of non-commutative differential geometry. In particular, we introduce a gravity action for a space-time which is the product of a four dimensional manifold by a two-point space. In the simplest…

The covariant canonical transformation theory applied to the relativistic Hamiltonian theory of classical matter fields in dynamical space-time yields a novel (first order) gauge field theory of gravitation. The emerging field equations…

In the quest of a physical theory of quantum gravity, spin foam models, or in short spinfoams, propose a well-defined path integral summing over quantized discrete space-time geometries. At the crossroad of topological quantum field theory,…