On Spectral Triples in Quantum Gravity I

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Standard

On Spectral Triples in Quantum Gravity I. / Aastrup, Johannes; M. Grimstrup, Jesper; Nest, Ryszard.

In: Journal of Noncommutative Geometry, Vol. 3, No. 1, 2009, p. 47-81.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Aastrup, J, M. Grimstrup, J & Nest, R 2009, 'On Spectral Triples in Quantum Gravity I', Journal of Noncommutative Geometry, vol. 3, no. 1, pp. 47-81.

APA

Aastrup, J., M. Grimstrup, J., & Nest, R. (2009). On Spectral Triples in Quantum Gravity I. Journal of Noncommutative Geometry, 3(1), 47-81.

Vancouver

Aastrup J, M. Grimstrup J, Nest R. On Spectral Triples in Quantum Gravity I. Journal of Noncommutative Geometry. 2009;3(1):47-81.

Author

Aastrup, Johannes ; M. Grimstrup, Jesper ; Nest, Ryszard. / On Spectral Triples in Quantum Gravity I. In: Journal of Noncommutative Geometry. 2009 ; Vol. 3, No. 1. pp. 47-81.

Bibtex

@article{df1cd4b0d69611dd9473000ea68e967b,
title = "On Spectral Triples in Quantum Gravity I",
abstract = "This paper establishes a link between Noncommutative Geometry and canonical quantum gravity. A semi-finite spectral triple over a space of connections is presented. The triple involves an algebra of holonomy loops and a Dirac type operator which resembles a global functional derivation operator. The interaction between the Dirac operator and the algebra reproduces the Poisson structure of General Relativity. Moreover, the associated Hilbert space corresponds, up to a discrete symmetry group, to the Hilbert space of diffeomorphism invariant states known from Loop Quantum Gravity. Correspondingly, the square of the Dirac operator has, in terms of canonical quantum gravity, the form of a global area-squared operator. Furthermore, the spectral action resembles a partition function of Quantum Gravity. The construction is background independent and is based on an inductive system of triangulations. This paper is the first of two papers on the subject.",
author = "Johannes Aastrup and {M. Grimstrup}, Jesper and Ryszard Nest",
note = "Keywords: hep-th; gr-qc",
year = "2009",
language = "English",
volume = "3",
pages = "47--81",
journal = "Journal of Noncommutative Geometry",
issn = "1661-6952",
publisher = "European Mathematical Society Publishing House",
number = "1",

}

RIS

TY - JOUR

T1 - On Spectral Triples in Quantum Gravity I

AU - Aastrup, Johannes

AU - M. Grimstrup, Jesper

AU - Nest, Ryszard

N1 - Keywords: hep-th; gr-qc

PY - 2009

Y1 - 2009

N2 - This paper establishes a link between Noncommutative Geometry and canonical quantum gravity. A semi-finite spectral triple over a space of connections is presented. The triple involves an algebra of holonomy loops and a Dirac type operator which resembles a global functional derivation operator. The interaction between the Dirac operator and the algebra reproduces the Poisson structure of General Relativity. Moreover, the associated Hilbert space corresponds, up to a discrete symmetry group, to the Hilbert space of diffeomorphism invariant states known from Loop Quantum Gravity. Correspondingly, the square of the Dirac operator has, in terms of canonical quantum gravity, the form of a global area-squared operator. Furthermore, the spectral action resembles a partition function of Quantum Gravity. The construction is background independent and is based on an inductive system of triangulations. This paper is the first of two papers on the subject.

AB - This paper establishes a link between Noncommutative Geometry and canonical quantum gravity. A semi-finite spectral triple over a space of connections is presented. The triple involves an algebra of holonomy loops and a Dirac type operator which resembles a global functional derivation operator. The interaction between the Dirac operator and the algebra reproduces the Poisson structure of General Relativity. Moreover, the associated Hilbert space corresponds, up to a discrete symmetry group, to the Hilbert space of diffeomorphism invariant states known from Loop Quantum Gravity. Correspondingly, the square of the Dirac operator has, in terms of canonical quantum gravity, the form of a global area-squared operator. Furthermore, the spectral action resembles a partition function of Quantum Gravity. The construction is background independent and is based on an inductive system of triangulations. This paper is the first of two papers on the subject.

M3 - Journal article

VL - 3

SP - 47

EP - 81

JO - Journal of Noncommutative Geometry

JF - Journal of Noncommutative Geometry

SN - 1661-6952

IS - 1

ER -

ID: 9396328