Details
| Original language | English |
|---|---|
| Article number | 215002 |
| Journal | Classical and quantum gravity |
| Volume | 33 |
| Issue number | 21 |
| Publication status | Published - 6 Oct 2016 |
Abstract
Quantum holonomy theory is a candidate for a non-perturbative theory of quantum gravity coupled to fermions. The theory is based on the QHD(M)-algebra, which essentially encodes how matter degrees of freedom are moved on a three-dimensional manifold. In this paper we commence the development of a lattice-independent formulation. We first introduce a flowdependent version of the QHD(M)-algebra and formulate necessary conditions for a state to exist hereon. We then use the GNS construction to build a kinematical Hilbert space. Finally, we find that operators, that correspond to the Dirac and gravitational Hamiltonians in a semi-classical limit, are background independent.
Keywords
- noncommutative geometry, quantum gravity, semi-classical limit, unified theory
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Physics and Astronomy (miscellaneous)
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In: Classical and quantum gravity, Vol. 33, No. 21, 215002, 06.10.2016.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On a lattice-independent formulation of quantum holonomy theory
AU - Aastrup, Johannes
AU - Grimstrup, Jesper Møller
PY - 2016/10/6
Y1 - 2016/10/6
N2 - Quantum holonomy theory is a candidate for a non-perturbative theory of quantum gravity coupled to fermions. The theory is based on the QHD(M)-algebra, which essentially encodes how matter degrees of freedom are moved on a three-dimensional manifold. In this paper we commence the development of a lattice-independent formulation. We first introduce a flowdependent version of the QHD(M)-algebra and formulate necessary conditions for a state to exist hereon. We then use the GNS construction to build a kinematical Hilbert space. Finally, we find that operators, that correspond to the Dirac and gravitational Hamiltonians in a semi-classical limit, are background independent.
AB - Quantum holonomy theory is a candidate for a non-perturbative theory of quantum gravity coupled to fermions. The theory is based on the QHD(M)-algebra, which essentially encodes how matter degrees of freedom are moved on a three-dimensional manifold. In this paper we commence the development of a lattice-independent formulation. We first introduce a flowdependent version of the QHD(M)-algebra and formulate necessary conditions for a state to exist hereon. We then use the GNS construction to build a kinematical Hilbert space. Finally, we find that operators, that correspond to the Dirac and gravitational Hamiltonians in a semi-classical limit, are background independent.
KW - noncommutative geometry
KW - quantum gravity
KW - semi-classical limit
KW - unified theory
UR - http://www.scopus.com/inward/record.url?scp=84991694329&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1602.06436
DO - 10.48550/arXiv.1602.06436
M3 - Article
AN - SCOPUS:84991694329
VL - 33
JO - Classical and quantum gravity
JF - Classical and quantum gravity
SN - 0264-9381
IS - 21
M1 - 215002
ER -