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The gauge field theories are usually quantized by fixing gauge. In this paper, we propose a new formalism that quantizes gauge fields without gauge fixing but naturally follows canonical formalism. New physical implications will follow.
It is argued that quantum gravity has an interpretation as a topological field theory provided a certain constraint from the path intergral measure is respected. The constraint forces us to couple gauge and matter fields to gravity for…
Invited contribution to the Encyclopedia of Mathematical Physics (2nd edition), providing an overview over some main ideas and results in quantum cosmology. Key points: Canonical quantisation of homogeneous, isotropic cosmology; discussion…
We investigate a connection between recent results in 3D quantum gravity, providing an effective noncommutative-spacetime description, and some earlier heuristic descriptions of a quantum-gravity contribution to the fuzziness of the…
The process of canonical quantization is redefined so that the classical and quantum theories coexist when \hbar>0, just as they do in the real world. This analysis not only supports conventional procedures, it also reveals new quantization…
Nonholonomic distributions and adapted fame structures on (pseudo) Riemannian manifolds of even dimension are employed to build structures equivalent to almost Kahler geometry and which allows to perform a Fedosov-like quantization of…
Quantum gravity places entirely new challenges on the formulation of a consistent theory as well as on an extraction of potentially observable effects. Quantum corrections due to the gravitational field are commonly expected to be tiny…
The geometro-stochastic method of quantization provides a framework for quantum general relativity, in which the principal frame bundles of local Lorentz frames that underlie the fibre-theoretical approach to classical general relativity…
If there exists a formulation of quantum mechanics which does not refer to a background classical spacetime manifold, it then follows as a consequence, (upon making one plausible assumption), that a quantum description of gravity should be…
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.…
We present a new approach to quantum gravity starting from Feynman's formulation for the simplest example, that of a scalar field as the representative matter. We show that we extend his treatment to a calculable framework using resummation…
The purpose of this paper is to introduce a new way to inquire the quantum cosmology for a certain gravitational theory. Normally, the quantum cosmological model is introduced as the minisuperspace theory which is obtained by reducing the…
We review some recent work by Carone, Erlich and Vaman on composite gravitons in metric-independent quantum field theories, with the aim of clarifying a number of basic issues. Focusing on a theory of scalar fields presented previously in…
It is shown that polymer quantization leads to a modified uncertainty principle similar to that obtained from string theory and non-commutative geometry. When applied to quantum field theory on general background spacetimes, corrections to…
A general definition has been proposed recently of a linear connection and a metric in noncommutative geometry. It is shown that to within normalization there is a unique linear connection on the quantum plane and there is no metric.
The expansion of our universe, when followed backward in time, implies that it emerged from a phase of huge density, the big bang. These stages are so extreme that classical general relativity combined with matter theories is not able to…
We develop a parameterized post-Friedmann (PPF) framework which describes three regimes of modified gravity models that accelerate the expansion without dark energy. On large scales, the evolution of scalar metric and density perturbations…
There are a number of approaches to testing General Relativity (GR) on linear scales using parameterized frameworks for modifying cosmological perturbation theory. It is sometimes assumed that the details of any given parameterization are…
Noncommutative field theories are a class of theories beyond the standard model of elementary particle physics. Their importance may be summarized in two facts. Firstly as field theories on noncommutative spacetimes they come with natural…
We argue that recent developments in discretizations of classical and quantum gravity imply a new paradigm for doing research in these areas. The paradigm consists in discretizing the theory in such a way that the resulting discrete theory…