Related papers: Towards the deformation quantization of linearized…
We outline, test, and apply a new scheme for nonpertubative analyses of quantized field systems in contact with dynamical gravity. While gravity is treated classically in the present paper, the approach lends itself for a generalization to…
In this article we study the quantization of a free real scalar field on a class of noncommutative manifolds, obtained via formal deformation quantization using triangular Drinfel'd twists. We construct deformed quadratic action functionals…
Recently one and two-parameter deformed Einstein equations have been studied for extremal quantum black holes which have been proposed to obey deformed statistics by Strominger. In this study, we give a deeper insight to the deformed…
We briefly discuss new models of an `affine' theory of gravity in multidimensional space-times with symmetric connections. We use and generalize Einstein's proposal to specify the space-time geometry by use of the Hamilton principle to…
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…
Building towards a more covariant approach to canonical classical and quantum gravity we outline an approach to constrained dynamics that de-emphasizes the role of the Hamiltonian phase space and highlights the role of the Lagrangian phase…
The current paper is dedicated to developing a (3+1) decomposition for the minimal gravitational Standard-Model Extension. Our setting is explicit diffeomorphism violation and we focus on the background fields known in the literature as $u$…
A deformation of Einstein Gravity is constructed based on gauging the noncommutative ISO(3,1) group using the Seiberg-Witten map. The transformation of the star product under diffeomorphism is given, and the action is determined to second…
We show that certain solutions to the linearized Einstein equation can---by the application of a particular type of linearized gauge transformation---be straightforwardly transformed into solutions of the exact Einstein equation. In cases…
Canonical methods can be used to construct effective actions from deformed covariance algebras, as implied by quantum-geometry corrections of loop quantum gravity. To this end, classical constructions are extended systematically to…
This is a collection of lectures given at the University of Heidelberg, especially but not exclusively for people who want to learn something about the canonical approach to quantum gravity, which is however not included in these lectures.…
We discuss the deformation quantization approach for the teaching of quantum mechanics. This approach has certain conceptual advantages which make its consideration worthwhile. In particular, it sheds new light on the relation between…
We study a noncommutative theory of gravity in the framework of torsional spacetime. This theory is based on a Lagrangian obtained by applying the technique of dimensional reduction of noncommutative gauge theory and that the yielded…
A Lagrange multiplier field can be used to restrict radiative corrections to the Einstein-Hilbert action to one-loop order. This result is employed to show that it is possible to couple a scalar field to the metric (graviton) field in such…
We generalise Langlois' Hamiltonian treatment of gauge-invariant linear cosmological perturbations to a cosmological setting with multiple scalar fields minimally coupled to gravity. We review the Hamilton-Jacobi-like technique for a…
In a class of generalized Einstein's gravity theories we derive the equations and general asymptotic solutions describing the evolution of the perturbed universe in unified forms. Our gravity theory considers general couplings between the…
We use the mathematical framework of loop quantum gravity (LQG) to study the quantization of three dimensional (Riemannian) gravity with positive cosmological constant (Lambda>0). We show that the usual regularization techniques (successful…
It is shown that target space diffeomorphism invariance of a generic Lagrangian for a set of scalar fields leads to an analog of Einstein equations for the geometry of a level set of these fields.
An approach to the quantization of gravity in the presence matter is examined which starts from the classical Einstein-Hilbert action and matter approximated by "point" particles minimally coupled to the metric. Upon quantization, the…
The quantum gravity is formulated based on principle of local gauge invariance. The model discussed in this paper has local gravitational gauge symmetry and gravitational field appears as gauge field. The problems on quantization and…