相关论文: Curvature from quantum deformations

Classical gravitational evolution admits an elegant and compact re-expression in terms of gauge covariant generalizations of Lie derivatives with respect to a spatial phase space dependent $su(2)$ valued vector field called the Electric…

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…

A consistent quantum theory of gravity has remained elusive ever since the emergence of General Relativity and Quantum Field Theory. Attempts to date have not yielded a candidate that is either free from problematic theoretical…

A semi-classical non-Hamiltonian model of a spontaneous collapse of unstable quantum system is given. The time evolution of the system becomes non-Hamiltonian at random instants of transition of pure states to reduced ones, given by a…

We construct a canonical quantization of the two dimensional theory of a parametrized scalar field on noncompact spatial slices. The kinematics is built upon generalized charge-network states which are labelled by smooth embedding…

Different versions of consistent canonical realizations of hypersurface deformations of spherically symmetric space-times have been derived in models of loop quantum gravity, modifying the classical dynamics and sometimes also the structure…

Stokes' theorem turns Abelian Berry phases into curvature fluxes, whereas path ordering precludes such a simple formula for non-Abelian holonomies. We show that a quantitative form of this intuition survives: arbitrary Wilczek--Zee…

We review discoveries in the nonlinear dynamics of curved spacetime, largely made possible by numerical solutions of Einstein's equations. We discuss critical phenomena and self-similarity in gravitational collapse, the behavior of…

Starting with assumptions both simple and natural from "physical" point of view we present a direct construction of transformations preserving wide class of (anti)commutation relations which describe Euclidean/Minkowski superspace…

In this paper we analyze the structure of some subalgebras of quantized enveloping algebras corresponding to unipotent and solvable subgroups of a simple Lie group G. These algebras have the non--commutative structure of iterated algebras…

We consider a Jordan domain diffeomorphic to a closed two-dimensional disk with a smooth boundary. Assuming the Gauss curvature of the domain has a negative lower bound, the Gauss-Bonnet formula provides an upper bound for the total…

Fuzzy geometry considered as the possible mathematical framework for reformulation of quantum-mechanical formalism in geometric terms. In this approach the states of massive particle m correspond to elements of fuzzy manifold called fuzzy…

The quantum fluctuations of the geodesic deviation equation in a flat background spacetime are discussed. We calculate the resulting mean squared fluctuations in the relative velocity and separation of test particles. The effect of these…

Canonical quantum gravity provides insights into the quantum dynamics as well as quantum geometry of space-time by its implications for constraints. Loop quantum gravity in particular requires specific corrections due to its quantization…

It is shown that the geometry of quantum theory can be derived from geometrical structure that may be considered more fundamental. The basic elements of this reconstruction of quantum theory are the natural metric on the space of…

We consider a curved space-time whose algebra of functions is the commutative limit of a noncommutative algebra and which has therefore an induced Poisson structure. In a simple example we determine a relation between this structure and the…

We consider general relativity with cosmological constant minimally coupled to electromagnetic field and assume that four-dimensional space-time manifold is the warped product of two surfaces with Lorentzian and Euclidean signature metrics.…

We review the superspace technique to determine supersymmetric spacetimes in the framework of off-shell formulations for supergravity in diverse dimensions using the case of 3D N=2 supergravity theories as an illustrative example. This…

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 a semi-classical approximation to the dynamics of a point particle in a noncommutative space. In this approximation, the noncommutativity of space coordinates is described by a Poisson bracket. For linear Poisson brackets, the…