Related papers: Canonical quantization of two-dimensional gravity
We give an introduction to the canonical formalism of Einstein's theory of general relativity. This then serves as the starting point for one approach to quantum gravity called quantum geometrodynamics. The main features and applications of…
A discussion of the meaning of a physical concept cannot be separated from discussion of the conditions for its ideal measurement. We assert that quantization is no more than the invocation of the quantum of action in the explanation of…
The cosmological constant problem is one of the long-standing issues of modern physics. While we can measure the value of the cosmological constant with great accuracy, we are not able to calculate it in a coherent theoretical framework. On…
A generalised canonical formulation of gravity is devised for foliations of spacetime with codimension $n\ge1$. The new formalism retains n-dimensional covariance and is especially suited to 2+2 decompositions of spacetime. It is also…
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 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.…
Loop Quantum Gravity provides a natural truncation of the infinite degrees of freedom of gravity, obtained by studying the theory on a given finite graph. We review this procedure and we present the construction of the canonical theory on a…
This paper gives a brief overview of the manifestly covariant canonical gauge gravity (CCGG) that is rooted in the De Donder-Weyl Hamiltonian formulation of relativistic field theories, and the proven methodology of the canonical…
A formalism previously introduced by the author using tesselated Cauchy surfaces is applied to define a quantized version of gravitating point particles in 2+1 dimensions. We observe that this is the first model whose quantum version…
We study some two-dimensional dilaton gravity models using the formal theory of partial differential equations. This allows us to prove that the reduced phase space is two-dimensional without an explicit construction. By using a convenient…
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…
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…
On the basis of dynamic quantization method we build in this paper a new mathematically correct quantization scheme of gravity. In the frame of this scheme we develop a canonical formalism in tetrad-connection variables in 4-D theory of…
Gravity theories with non-minimally coupled scalar fields are used as characteristic examples in order to demonstrate the challenges, pitfalls and future perspectives of considering alternatives to general relativity. These lecture notes…
A unified theory of four-dimensional gravity together with the standard model is presented, with supersymmetry breaking of M-theory at a TeV. Masses of the the known particles are derived. The cosmological constant is quantum generated to…
A three dimensional generally covariant theory is described that has a 2+1 canonical decomposition in which the Hamiltonian constraint, which generates the dynamics, is absent. Physical observables for the theory are described and the…
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…
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…
In two dimensions a large class of gravitational systems including, e.g., $R^2$-gravity can be quantized exactly also when coupled dynamically to a Yang-Mills theory. Some previous considerations on the quantization of pure gravity theories…
We carry out the canonical analysis of a covariant version of unimodular gravity in terms of the connection representation. We then proceed to quantize this theory by implementing the Dirac procedure. We confirm whether and how the Kodama…