Gravitation in terms of observables 2: the algebra of fundamental observables (original) (raw)
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Gravitation in terms of observables
Classical and Quantum Gravity, 2018
In the 1960's, Mandelstam proposed a new approach to gauge theories and gravity based on loops. The program was completed for Yang-Mills theories by Gambini and Trias in the 1980's. In this approach, gauge theories could be understood as representations of certain group: the group of loops. The same formalism could not be implemented at that time for the gravitational case. Here we would like to propose an extension to the case of gravity. The resulting theory is described in terms of loops and open paths and can provide the underpinning for a new quantum representation for gravity distinct from the one used in loop quantum gravity or string theory. In it, space-time points are emergent entities that would only have quasi-classical status. The formulation may be given entirely in terms of Dirac observables that form a set of gauge invariant functions that completely define the Riemannian geometry of the spacetime. At the quantum level this formulation will lead to a reduced phase space quantization free of any constraints.
Observables in quantum gravity
We study a family of physical observable quantities in quantum gravity. We denote them W functions, or n-net functions. They represent transition amplitudes between quantum states of the geometry, are analogous to the n-point functions in quantum field theory, but depend on spin networks with n connected components. In particular, they include the three-geometry to three-geometry transition amplitude. The W functions are scalar under four-dimensional diffeomorphism, and fully gauge invariant. They capture the physical content of the quantum gravitational theory.
A Gauge-theoretical Treatment of the Gravitational Field: Classical
2008
In the geometrodynamical setting of general relativity one is concerned mainly with Riemannian metrics over a manifold M . We show that for the space M := Riem(M), we have a natural principal fiber bundle (PFB) structure Diff(M) →֒ M π → M/Diff(M), first hinted at in [1]. This construction makes the gravitational field amenable to exactly the same gauge-theoretic treatment given in [2], where it is used to separate rotational and vibrational degrees of freedom of n-particle systems, both classically and quantum mechanically. Furthermore, we show how the gauge connection in this PFB setting can be seen as a realization of Mach’s Principle of Relative Motion, in accordance with Barbour’s et al work on timeless gravitational theories [3] using best-matching. We show Barbour’s reconstruction of GR is obtained by requiring the connection to be the one induced by the deWitt metric in M. As a simple application of the gauge theory, we put the ADM lagrangian in a Kaluza-Klein context, in wh...
Gravity quantized: Loop quantum gravity with a scalar field
2010
but we do not have quantum gravity." This phrase is often used when analysis of a physical problem enters the regime in which quantum gravity effects should be taken into account. In fact, there are several models of the gravitational field coupled to (scalar) fields for which the quantization procedure can be completed using loop quantum gravity techniques. The model we present in this paper consist of the gravitational field coupled to a scalar field. The result has similar structure to the loop quantum cosmology models, except for that it involves all the local degrees of freedom of the gravitational field because no symmetry reduction has been performed at the classical level. PACS numbers: 4.60.Pp; 04.60.-m; 03.65.Ta; 04.62.+v
2009
One of the main challenges in theoretical physics over the last five decades has been to reconcile quantum mechanics with general relativity into a theory of quantum gravity. However, such a theory has been proved to be hard to attain due to i) conceptual difficulties present in both the component theories (General Relativity (GR) and Quantum Theory); ii) lack of experimental evidence, since the regimes at which quantum gravity is expected to be applicable are far beyond the range of conceivable experiments. Despite these difficulties, various approaches for a theory of Quantum Gravity have been developed. In this thesis we focus on two such approaches: Loop Quantum Gravity and the Topos theoretic approach. The choice fell on these approaches because, although they both reject the Copenhagen interpretation of quantum theory, their underpinning philosophical approach to formulating a quantum theory of gravity are radically different. In particular LQG is a rather conservative scheme,...
Observables in classical canonical gravity: Folklore demystified
Journal of Physics: Conference Series, 2010
We give an overview of some conceptual difficulties, sometimes called paradoxes, that have puzzled for years the physical interpetation of classical canonical gravity and, by extension, the canonical formulation of generally covariant theories. We identify these difficulties as stemming form some terminological misunderstandings as to what is meant by "gauge invariance", or what is understood classically by a "physical state". We make a thorough analysis of the issue and show that all purported paradoxes disappear when the right terminology is in place. Since this issue is connected with the search of observables -gauge invariant quantities -for these theories, we formally show that time evolving observables can be constructed for every observer. This construction relies on the fixation of the gauge freedom of diffeomorphism invariance by means of a scalar coordinatization. We stress the condition that the coordinatization must be made with scalars. As an example of our method for obtaining observables we discuss the case of the massive particle in AdS spacetime.
Gauge theory of quantum gravity
2014
The gravity is classically formulated as the geometric curvature of the space-time in general relativity which is completely different from the other well-known physical forces. Since seeking a quantum framework for the gravity is a great challenge in physics. Here we present an alternative construction of quantum gravity in which the quantum gravitational degrees of freedom are described by the non-Abelian gauge fields characterizing topological non-triviality of the space-time. The quantum dynamics of the space-time thus corresponds to the superposition of the distinct topological states. Its unitary time evolution is described by the path integral approach. This result will also be suggested to solve some major problems in physics of the black holes.
Quantum gravity: an introduction to some recent results
Reviews of Modern Physics, 1989
This article presents a general overview of the problems involved in the application of the quantum principle to a theory of gravitation. The ultraviolet divergences that appear in any perturbative computation are reviewed in some detail, and it is argued that it is unlikely that any theory based on local quantum fields could be consistent. This leads in a natural way to a supersymmetric theory of extended objects as the next candidate theory to study. An elementary introduction to superstrings closes the review, and some speculations about the most promising avenues of research are offered. CONTENTS Gravitational Fields III. Einstein Gravity as a Gauge Theory. Perturbative Results at One and Two Loops A. Gravity as a gauge theory B. The method of the background field C. The one-loop computation of 't Hooft and Veltman D. The two-loop computation of Goro6'and Sagnotti IV. Ultraviolet Divergences in a Quantum Field Theory of Gravity V. Canonical Formalism: The Wheeler-De%'itt Equation VI. The Semiclassical Approximation: Schrodinger s Equation VII. Some Specific Boundary Conditions. Toy Models in Quantum Cosmology A. The de Sitter model of Hartle and Hawking B. The effect of conformally invariant scalars in the toy model C. A cosmological model of Banks VIII. Quantum Gravity in the General Framework of Superstring Theories A. Gravity from strings B. Modular invariance C. Gravity in the long-wavelength limit D.
On the correspondence between classical and quantum gravity
Classical and Quantum Gravity, 2001
The relationship between the classical and quantum theories of gravity is reexamined. The value of the gravitational potential defined with the help of the two-particle scattering amplitudes is shown to be in disagreement with the classical result of General Relativity given by the Schwarzschild solution. It is shown also that the potential so defined fails to describe whatever non-Newtonian interactions of macroscopic bodies. An alternative interpretation of theh 0-order part of the loop corrections is given directly in terms of the effective action. Gauge independence of that part of the one-loop radiative corrections to the gravitational form factors of the scalar particle is proved, justifying the interpretation proposed.