相关论文: Canonical Quantization of Spherically Symmetric Gr…

A new representation for canonical gravity and supergravity is presented, which combines advantages of Ashtekar's and the Wheeler~DeWitt representation: it has a nice geometric structure and the singular metric problem is absent. A formal…

The present article summarizes the work of the papers \cite{1} dealing with the quantization of pure gravity and gravity coupled to a Maxwell field and a cosmological constant in presence of spherical symmetry. The class of models presented…

It is shown - in Ashtekar's canonical framework of General Relativity - that spherically symmetric (Schwarzschild) gravity in 4 dimensional space-time constitutes a finite dimensional completely integrable system. Canonically conjugate…

We perform canonical quantization of gravity in the background of a Schwarzschild black hole in the generalized Regge-Wheeler gauge proposed in \cite{Kallosh:2021ors}. We find that the Hamiltonian at the quadratic level is unitary and…

Stationary spherically symmetric gravity is equivalent to a nonlinear coset sigma model on SL(2,R)/SO(2) coupled to a gravitational remnant. Classically there are stationary solutions besides the static Schwarzschild metric labeled by the…

The preceding talks given at this conference have dealt mainly with general ideas for, main problems of and techniques for the task of quantizing gravity canonically. Since one of the major motivations to arrange for this meeting was that…

Canonical quantization of spherically symmetric space-times is carried out, using real-valued densitized triads and extrinsic curvature components, with specific factor ordering choices ensuring in an anomaly free quantum constraint…

We study the deformation (Moyal) quantisation of gravity in both the ADM and the Ashtekar approach. It is shown, that both can be treated, but lead to anomalies. The anomaly in the case of Ashtekar variables, however, is merely a central…

Using self dual Ashtekar variables, we investigate (at the effective level) the spherically symmetry reduced model of loop quantum gravity, both in vacuum and when coupled to a scalar field. Within the real Ashtekar-Barbero formulation, the…

We construct a weave state which approximates a degenerate 3-metric of rank 2 at large scales. It turns out that a non-degenerate metric region can be evolved from this degenerate metric by the classical Ashtekar equations, hence the…

The canonical analysis and subsequent quantization of the (2+1)-dimensional action of pure gravity plus a cosmological constant term is considered, under the assumption of the existence of one spacelike Killing vector field. The proper…

We introduce a reduced model for a real sector of complexified Ashtekar gravity that does not correspond to a subset of Einstein's gravity but for which the programme of canonical quantization can be carried out completely, both, via the…

The 3+1 (canonical) decomposition of all geometries admitting two-dimensional space-like surfaces is exhibited. A proposal consisting of a specific re-normalization {\bf Assumption} and an accompanying {\bf Requirement} is put forward,…

In this paper we have carried out a transformation from Ashtekar's theory of GR into a reduced theory where the physical degrees of freedom are explicit. We have performed the canonical analysis, computed the classical dynamics and have…

The non-perturbative canonical quantization of the N=1 supergravity with the non-zero cosmological constant is studied using the Ashtekar formalism. A semi-classical wave function is obtained and it has the form of the exponential of the…

We present here the canonical treatment of spherically symmetric (quantum) gravity coupled to spherically symmetric Maxwell theory with or without a cosmological constant. The quantization is based on the reduced phase space which is…

We extend here the canonical treatment of spherically symmetric (quantum) gravity to the most simple matter coupling, namely spherically symmetric Maxwell theory with or without a cosmological constant. The quantization is based on the…

We quantize the Hamilton equations instead of the Hamilton condition. The resulting equation has the simple form $-\D u=0$ in a fiber bundle, where the Laplacian is the Laplacian of the Wheeler-DeWitt metric provided $n\not=4$. Using then…

We write down a quantum gravity equation which generalizes the Wheeler-DeWitt one in view of including a time dependence in the wave functional. The obtained equation provides a consistent canonical quantization of the 3-geometries…

We construct a limit of Hamiltonian gravity as the determinant of the spatial triad (and hence of the four-metric) goes to zero. Within the Barbero-Immirzi SU (2) formulation, we present two possible realizations of this limit, with the…