Related papers: Timelike twisted geometries
Based on a recent purely geometric construction of observables for the spatial diffeomorphism constraint, we propose two distinct quantum reductions to spherical symmetry within full 3+1-dimensional loop quantum gravity. The construction of…
Spin Foam and Loop approaches to Quantum Gravity reformulate Einstein's theory of relativity in terms of connection variables. The metric properties are encoded in face bivectors/conjugate fluxes that are required to satisfy certain…
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…
We study the quantum matrix algebra $R_{21}x_1x_2=x_2x_1 R$ and for the standard $2\times 2$ case propose it for the co-ordinates of $q$-deformed Euclidean space. The algebra in this simplest case is isomorphic to the usual quantum matrices…
In previous works, we showed that both time and space can emerge from entanglement within a globally constrained quantum Universe, with no background coordinates. By extending the Page and Wootters quantum time formalism to include both…
We derive a spacetime formulation of quantum general relativity from (hamiltonian) loop quantum gravity. In particular, we study the quantum propagator that evolves the 3-geometry in proper time. We show that the perturbation expansion of…
After dimensional reduction the stationary spherically symmetric sector of Einstein's gravity is identified with an SL(2,R)/SO(2) Sigma model coupled to a one dimensional gravitational remnant. The space of classical solutions consists of a…
We show how quantum fields can be used to measure the curvature of spacetime. In particular, we find that knowledge of the imprint that spacetime curvature leaves in the correlators of quantum fields suffices, in principle, to reconstruct…
We study a generalized version of the Hamiltonian constraint operator in nonperturbative loop quantum gravity. The generalization is based on admitting arbitrary irreducible SU(2) representations in the regularization of the operator, in…
In this work, we study the classical and quantum properties of the unique commutative Lorentz-covariant connection for loop quantum gravity. This connection has been found after solving the second-class constraints inherited from the…
The problem of singularities associated with Dirac strings and closed timelike curves in classical solutions of pure gravity is analyzed here. A method to eliminate these is introduced and established first for the Taub-NUT geometry. This…
Certain difficulties of quantum gravity can be avoided if we embed the spacetime $V_4$ into a higher dimensional space $V_N$; then our spacetime is merely a 4-surface in $V_N$.What remains is conceptually not so difficult: just to quantise…
We use the polygon representation of 2+1--dimensional gravity to explicitly carry out the canonical quantization of a universe with the topology of a torus. The mapping-class-invariant wave function for a quantum ''big bounce'', is…
We quantize spherically symmetric electrovacuum gravity. The algebra of Hamiltonian constraints can be made Abelian via a rescaling and linear combination with the diffeomorphism constraint. As a result the constraint algebra is a true Lie…
If one replaces the constraints of the Ashtekar-Barbero $SU(2)$ gauge theory formulation of Euclidean gravity by their $U(1)^3$ version, one arrives at a consistent model which captures significant structure of its $SU(2)$ version. In…
A model for 2D Quantum Gravity is constructed out of the Virasoro group. To this end the quantization of the abstract Virasoro group is revisited. For the critical values of the conformal anomaly c, some quantum operators (SL(2,R)…
We consider the quantization of gravity as an SL(2,C) gauge theory in terms of Ashtekar's selfdual variables and reality conditions for the spatial metric (RCI) and its evolution (RCII). We start from a holomorphic phase space formulation.…
We summarize our work on spherically symmetric midi-superspaces in loop quantum gravity. Our approach is based on using inhomogeneous slicings that may penetrate the horizon in case there is one and on a redefinition of the constraints so…
This work is developed in the context of Lorentzian spin-foams with space- and time-like boundaries. It is argued that the equations describing the semiclassical regime of the various spin-foam amplitudes admit a common biquaternionic…
For quantum field theory on curved spacetimes, a critical role is played by their foliation into spacelike time-slices at each value $t$ of a coordinate time, with corresponding metric in ADM form. We provide a general construction for the…