GRAVITONS AS EMBROIDERY ON THE WEAVE
Abstract
We investigate the physical interpretation of the loop states that appear in the loop representation of quantum gravity. By utilizing the “weave” state, which has been recently introduced as a quantum description of the microstructure of flat space, we analyze the relation between loop states and graviton states. This relation determines a linear map M from the state-space of the nonperturbative theory (loop space) into the state-space of the linearized theory (Fock space). We present an explicit form of this map, and a preliminary investigation of its properties. The existence of such a map indicates that the full nonperturbative quantum theory includes a sector that describes the same physics as (the low energy regimes of) the linearized theory, namely gravitons on flat space.
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Previous work [9,10,27] showed spin network states provide a natural orthogonal decomposition of H̃_o into finite dimensional subspaces.
“The previous work showed that the spin network states provide us with a natural orthogonal decomposition of the Hilbert space ˜ H o of gauge invariant states in to fi nite dimensional sub-spaces.”
From Quantum theory of geometry: I. Area operators (1997) · cites this paper as [27]
The explicit calculation of the Temperley-Lieb trace of a trivalent spin network is generally based on a generalization of the chromatic method of spin-network evaluation.
“The explicit calculation of the trace is generally based on a generalization of the chromatic method of spin-network evaluation [60].”
From Geometry eigenvalues and the scalar product from recoupling theory in loop quantum gravity (1996) · cites this paper as [60]
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Ashtekar, A., & Lewandowski, J. (1997) · Classical and Quantum Gravity · doi:10.1088/0264-9381/14/1a/006 · Cited by 852 · see citing works
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- Authors
- IWASAKI, J., & ROVELLI, C.
- Affiliations
- University of Pittsburgh (US)
- Physics Dept. University of Pittsburgh, Pittsburgh, PA 15260, USA
- ORCID
- IWASAKI, JUNICHI
- Venue
- International Journal of Modern Physics D
- Publisher
- World Scientific Pub Co Pte Lt
- Published
- 1992-01
- Volume
- 01
- Issue
- 03n04
- Pages
- 533-557
- ISSN
- 0218-2718 (ISSN-L)
- 1793-6594
- OpenAlex
- W2017596718
- Cited by
- 47
- References
- 0
- Citations by year
- 2022: 1 · 2014: 1 · 2013: 1 · 2012: 4
- FWCI
- 1.96
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- International Journal of Modern Physics D (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- loop quantum gravity, graviton, linearized gravity, Fock space, non-perturbative quantum gravity, low-energy limit
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