Quantum theory of geometry: I. Area operators
Abhay Ashtekar,Jerzy Lewandowski +1 more
Reads0
Chats0
TLDR
In this article, a functional calculus for quantum geometry is developed for a fully nonperturbative treatment of quantum gravity, which is used to begin a systematic construction of a quantum theory of geometry, and Regulated operators corresponding to 2-surfaces are introduced and shown to be self-adjoint on the underlying (kinematical) Hilbert space of states.Abstract:
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces are introduced and shown to be self-adjoint on the underlying (kinematical) Hilbert space of states. It is shown that their spectra are purely discrete, indicating that the underlying quantum geometry is far from what the continuum picture might suggest. Indeed, the fundamental excitations of quantum geometry are one dimensional, rather like polymers, and the three-dimensional continuum geometry emerges only on coarse graining. The full Hilbert space admits an orthonormal decomposition into finite-dimensional subspaces which can be interpreted as the spaces of states of spin systems. Using this property, the complete spectrum of the area operators is evaluated. The general framework constructed here will be used in a subsequent paper to discuss three-dimensional geometric operators, e.g. the ones corresponding to volumes of regions.read more
Citations
More filters
Dissertation
New dynamics for canonical loop quantum gravity
TL;DR: In this paper, the authors present a new approach for quantizing the Hamiltonians in various LQG models, which is based on novel regularization procedures of the classical functionals, starting with the construction of a new geometrical operator, the curvature operator, related to the threedimensional Ricci curvature.
Dissertation
Modèles de mousses de spin pour la gravité quantique en 3 dimensions
TL;DR: In this article, the authors present a set of results for the modeles of mousses de spin for gravite quantique in 3 dimensions, including an invariant of Ponzano-Regge and Chern-Simons.
Posted Content
On the fundamental length of quantum geometry and the black hole entropy
TL;DR: In this paper, it was shown that the black hole entropy derived from quantum geometry in the limit of classical geometry is completely consistent with the Bekenstein-Hawking form in the extremal limit of 1-puncture states of the quantum surface geometry.
Posted Content
Corrections to the Bekenstein-Hawking entropy and the Hawking radiation spectrum
Brian Kong,Youngsub Yoon +1 more
TL;DR: In this article, a new area spectrum based on the norm of Ashtekar's variables was proposed, which is mathematically consistent and almost correctly predicts the Bekenstein-Hawking entropy without adjusting the Immirzi parameter.
Dissertation
Structure chirale de la gravité quantique à boucles
TL;DR: The relativite generale represente la description la plus precise de l'interaction gravitationnelle as mentioned in this paper, i.e., the description that is the most precise of all the descriptions of gravitation.
References
More filters
Journal ArticleDOI
Discreteness of area and volume in quantum gravity
Carlo Rovelli,Lee Smolin +1 more
TL;DR: In this article, the authors studied the spectrum of the volume in nonperturbative quantum gravity, and showed that the spectrum can be computed by diagonalizing finite dimensional matrices, which can be seen as a generalization of the spin networks.
Journal ArticleDOI
New Hamiltonian formulation of general relativity
TL;DR: An important feature of the new form of constraints is the natural embedding of the constraint surface of the Einstein phase space into that of Yang-Mills phase space, which provides new tools to analyze a number of issues in both classical and quantum gravity.
Book
Lectures on Non-Perturbative Canonical Gravity
TL;DR: In this article, the authors present an up-to-date account of a non-perturbative, canonical quantization program for gravity, which was highlighted in virtually every major conference in gravitational physics over the past three years.
Journal ArticleDOI
Loop space representation of quantum general relativity
TL;DR: In this article, the authors define a new representation for quantum general relativity, in which exact solutions of the quantum constraints may be obtained, by means of a noncanonical graded Poisson algebra of classical observables, defined in terms of Ashtekar's new variables.
Journal ArticleDOI
Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
TL;DR: In this article, a quantization of diffeomorphism invariant theories of connections is studied and the quantum diffeomorphicism constraint is solved and the space of solutions is equipped with an inner product that is shown to satisfy the physical reality conditions.