相关论文: Quantum gravity on polygons and $\Bbb R\times \Bbb…

We review quantum gravity model building using the new formalism of `quantum Riemannian geometry' to construct this on finite discrete spaces and on fuzzy ones such as matrix algebras. The formalism starts with a `differential structure' as…

Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…

We consider functional-integral quantisation of the moduli of all quantum metrics defined as square-lengths $a$ on the edges of a Lorentzian square graph. We determine correlation functions and find a fixed relative uncertainty $\Delta…

In loop quantum cosmology, Friedmann-LeMaitre-Robertson-Walker (FLRW) space-times arise as well-defined approximations to specific \emph{quantum} geometries. We initiate the development of a quantum theory of test scalar fields on these…

3-dimensional gravity coupled to Maxwell (or Klein-Gordon) fields is exactly soluble under the assumption of axi-symmetry. The solution is used to probe several quantum gravity issues. In particular, it is shown that the quantum…

The higher dimensional Quantum General Relativity of a Riemannian manifold being an embedded space in a space-time being a Lorentzian manifold is investigated. The model of quantum geometrodynamics, based on the Wheeler-DeWitt equation…

We study the quantum geometry of the fuzzy sphere defined as the angular momentum algebra $[x_i,x_j]=2\imath\lambda_p \epsilon_{ijk}x_k$ modulo setting $\sum_i x_i^2$ to a constant, using a recently introduced 3D rotationally invariant…

We provide a relatively self-contained introduction to the application of quantum spacetime and quantum Riemannian geometry to theoretical physics. Recent successes include calculation of the vacuum energy of spacetime curvature…

We study a new approach to generally covariant quantum mechanics applied in the case of an FLRW cosmological background. For positive spatial curvature we find a discrete series of solutions of the Klein-Gordon equation that can reasonably…

We revisit the construction of quantum Riemannian geometries on graphs starting from a hermitian metric compatible connection, which always exists. We use this method to find quantum Levi-Civita connections on the $n$-leg star graph for…

We construct noncommutative or `quantum' Riemannian geometry on the integers $\Bbb Z$ as a lattice line $\cdots\bullet_{i-1}-\bullet_i-\bullet_{i+1}\cdots$ with its natural 2-dimensional differential structure and metric given by arbitrary…

We propose and solve mathematically a simple euclidean model for quantum gravity in one dimension. In the case of an open curve, the continuum limit is trivial, that is, the size of the universe is infinite, independently of the value of…

We review some recent attempts to extract information about the nature of quantum gravity, with and without matter, by quantum field theoretical methods. More specifically, we work within a covariant lattice approach where the individual…

We construct an extension of standard flat FLRW cosmology with matter, possessing local D = 1, N = 1 proper-time supersymmetry. The fundamental equation for the resulting mini-superspace models of quantum universes is a Dirac-like analogue…

Exactly soluble models can serve as excellent tools to explore conceptual issues in non-perturbative quantum gravity. In perturbative approaches, it is only the two radiative modes of the linearized gravitational field that are quantized.…

No theory of four-dimensional quantum gravity exists as yet. In this situation the two-dimensional theory, which can be analyzed by conventional field-theoretical methods, can serve as a toy model for studying some aspects of quantum…

The linearized Einstein field equations provide a low-energy wave equation for the propagation of gravitational fields which may originate from a high energy source. Motivated by loop quantum gravity, we propose the polymer quantization…

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…

Loop Quantum Gravity faces challenges in constructing a well-defined Hamiltonian constraint and understanding the quantum notion of time. In this paper these issues are studied by quantizing the $U(1)^3$ model, a simplified system…

We propose a model of quantum gravity in arbitrary dimensions defined in terms of the BV quantization of a supersymmetric, infinite dimensional matrix model. This gives an (AKSZ-type) Chern-Simons theory with gauge algebra the space of…