Related papers: Quantizing canonical gravity in the real domain
We use a canonical parametrization of twisted geometries describing the classical phase space of loop quantum gravity on a fixed graph, and establish its explicit correspondence with the associated frame bases and spinorial descriptions.…
This short note is devoted to the Hamiltonian analysis of the normalized general relativity and recently proposed model of vacuum energy sequestering. The common property of these models is the presence of the global variables. We discuss…
We review an attempt to set a suitable foundational principle for consistent quantization of gravity based on the canonical formulation. It requires extending the spacetime description of the relativistic postulates to also encompass an…
The Wilson loop functionals in terms of Ashtekar's variables were the first (formal) solutions to the quantized hamiltonian constraint of canonical gravity. Here it is shown that the same functionals also solve the supergravity constraints…
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…
Two different Hamiltonian formulations of the metric gravity are discussed and applied to describe a free gravitational field in the $d$ dimensional Riemann space-time. Theory of canonical transformations, which relate equivalent…
Different aspects of relativity, mainly in a canonical formulation, relevant for the question "Is spacetime nothing more than a mathematical space (which describes the evolution in time of the ordinary three-dimensional world) or is it a…
A covariant Hamiltonian description was introduced in the dynamics of charges and electromagnetic interaction. By a canonical transformation this Hamiltonian formalism was transformed to obtain the Dirac generators for any form of…
The Lagrangian formulation of classical field theories and in particular general relativity leads to a coordinate-free, fully covariant analysis of these constrained systems. This paper applies multisymplectic techniques to obtain the…
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…
General relativity becomes vastly simpler in three spacetime dimensions: all vacuum solutions have constant curvature, and the moduli space of solutions can be almost completely characterized. As a result, this lower dimensional setting…
Canonical quantization of gravity in general relativity is greatly simplified by the artificial decomposition of space and time into a 3+1 formalism. Such a simplification may appear to come at the cost of general covariance. This requires…
General aspects of vielbein representation, ADM formulation and canonical quantization of gravity are reviewed using pure gravity in three dimensions as a toy model. The classical part focusses on the role of observers in general…
A detailed canonical analysis for three-dimensional massive gravity is performed. The construction of the fundamental Dirac brackets, the complete structure of the constraints and the counting of the physical degrees of freedom are…
Classical physics is reformulated as a constrained Hamiltonian system in the history phase space. Dynamics, i.e. the Euler-Lagrange equations, play the role of first-class constraints. This allows us to apply standard methods from the…
The quantization of Lorentzian or Euclidean 2+1 gravity by canonical methods is a well-studied problem. However, the constraints of 2+1 gravity are those of a topological field theory and therefore resemble very little those of the…
Canonical transformations relating the variables of the ADM-, Ashtekar's and Witten's formulations of gravity are computed in 2+1~dimensions. Three different forms of the BRST-charge are given in the 2+1 dimensional Ashtekar formalism, two…
I suggest in this letter a new strategy to attack the problem of the reality conditions in the Ashtekar approach to classical and quantum general relativity. By writing a modified Hamiltonian constraint in the usual $SO(3)$ Yang-Mills phase…
The nature of the classical canonical phase-space variables for gravity suggests that the associated quantum field operators should obey affine commutation relations rather than canonical commutation relations. Prior to the introduction of…
For spacetimes with the topology $\IR\!\times\!T^2$, the action of (2+1)-dimensional gravity with negative cosmological constant $\La$ is written uniquely in terms of the time-independent traces of holonomies around two intersecting…