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  Quantum theory of geometry: I. Area operators

Ashtekar, A., & Lewandowski, J. (1997). Quantum theory of geometry: I. Area operators. Classical and Quantum Gravity, 14(1A), A55-A81.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-5ACB-3 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-5ACC-1
Genre: Journal Article

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quantum-2.pdf (Publisher version), 212KB
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 Creators:
Ashtekar, Abhay, Author
Lewandowski, Jerzy1, Author
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1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              

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 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.

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 Dates: 1997-01
 Publication Status: Published in print
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 Identifiers: eDoc: 330161
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Title: Classical and Quantum Gravity
  Alternative Title : Class. Quant. Grav.
Source Genre: Journal
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Pages: - Volume / Issue: 14 (1A) Sequence Number: - Start / End Page: A55 - A81 Identifier: ISSN: 0264-9381