Details
| Original language | English |
|---|---|
| Article number | 1800080 |
| Number of pages | 14 |
| Journal | Fortschritte der Physik |
| Volume | 67 |
| Issue number | 4 |
| Publication status | Published - 8 Apr 2019 |
Abstract
In this paper we establish the existence of the non-perturbative theory of quantum gravity known as quantum holonomy theory by showing that a Hilbert space representation of the QHD(M) algebra, which is an algebra generated by holonomy-diffeomorphisms and by translation operators on an underlying configuration space of connections, exist. We construct operators, which correspond to the Hamiltonian of general relativity and the Dirac Hamiltonian, and show that they give rise to their classical counterparts in a classical limit. We also find that the structure of an almost-commutative spectral triple emerge in the same limit. The Hilbert space representation, that we find, is non-local, which appears to rule out spacial singularities such as the big bang and black hole singularities. Finally, the framework also permits an interpretation in terms of non-perturbative Yang-Mills theory as well as other non-perturbative quantum field theories. This paper is the first of two, where the second paper contains mathematical details and proofs.
Keywords
- mathematical physics, non-perturbative, noncommutative geometry, quantum gravity
ASJC Scopus subject areas
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In: Fortschritte der Physik, Vol. 67, No. 4, 1800080, 08.04.2019.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On Representations of the Quantum Holonomy Diffeomorphism Algebra
AU - Aastrup, Johannes
AU - Grimstrup, Jesper Møller
N1 - Funding Information: This work is financially supported by Ilyas Khan, St EdmundÕs College, Cambridge, United Kingdom.
PY - 2019/4/8
Y1 - 2019/4/8
N2 - In this paper we establish the existence of the non-perturbative theory of quantum gravity known as quantum holonomy theory by showing that a Hilbert space representation of the QHD(M) algebra, which is an algebra generated by holonomy-diffeomorphisms and by translation operators on an underlying configuration space of connections, exist. We construct operators, which correspond to the Hamiltonian of general relativity and the Dirac Hamiltonian, and show that they give rise to their classical counterparts in a classical limit. We also find that the structure of an almost-commutative spectral triple emerge in the same limit. The Hilbert space representation, that we find, is non-local, which appears to rule out spacial singularities such as the big bang and black hole singularities. Finally, the framework also permits an interpretation in terms of non-perturbative Yang-Mills theory as well as other non-perturbative quantum field theories. This paper is the first of two, where the second paper contains mathematical details and proofs.
AB - In this paper we establish the existence of the non-perturbative theory of quantum gravity known as quantum holonomy theory by showing that a Hilbert space representation of the QHD(M) algebra, which is an algebra generated by holonomy-diffeomorphisms and by translation operators on an underlying configuration space of connections, exist. We construct operators, which correspond to the Hamiltonian of general relativity and the Dirac Hamiltonian, and show that they give rise to their classical counterparts in a classical limit. We also find that the structure of an almost-commutative spectral triple emerge in the same limit. The Hilbert space representation, that we find, is non-local, which appears to rule out spacial singularities such as the big bang and black hole singularities. Finally, the framework also permits an interpretation in terms of non-perturbative Yang-Mills theory as well as other non-perturbative quantum field theories. This paper is the first of two, where the second paper contains mathematical details and proofs.
KW - mathematical physics
KW - non-perturbative
KW - noncommutative geometry
KW - quantum gravity
UR - http://www.scopus.com/inward/record.url?scp=85061051551&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1709.02943
DO - 10.48550/arXiv.1709.02943
M3 - Article
AN - SCOPUS:85061051551
VL - 67
JO - Fortschritte der Physik
JF - Fortschritte der Physik
SN - 0015-8208
IS - 4
M1 - 1800080
ER -