Details
| Original language | English |
|---|---|
| Pages (from-to) | 783-818 |
| Number of pages | 36 |
| Journal | Fortschritte der Physik |
| Volume | 64 |
| Issue number | 10 |
| Early online date | 12 Sept 2016 |
| Publication status | E-pub ahead of print - 12 Sept 2016 |
Abstract
We present quantum holonomy theory, which is a non-perturbative theory of quantum gravity coupled to fermionic degrees of freedom. The theory is based on a (Formula presented.) -algebra that involves holonomy-diffeo-morphisms on a 3-dimensional manifold and which encodes the canonical commutation relations of canonical quantum gravity formulated in terms of Ashtekar variables. Employing a Dirac type operator on the configuration space of Ashtekar connections we obtain a semi-classical state and a kinematical Hilbert space via its GNS construction. We use the Dirac type operator, which provides a metric structure over the space of Ashtekar connections, to define a scalar curvature operator, from which we obtain a candidate for a Hamilton operator. We show that the classical Hamilton constraint of general relativity emerges from this in a semi-classical limit and we then compute the operator constraint algebra. Also, we find states in the kinematical Hilbert space on which the expectation value of the Dirac type operator gives the Dirac Hamiltonian in a semi-classical limit and thus provides a connection to fermionic quantum field theory. Finally, an almost-commutative algebra emerges from the holonomy-diffeomorphism algebra in the same limit.
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In: Fortschritte der Physik, Vol. 64, No. 10, 12.09.2016, p. 783-818.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Quantum holonomy theory
AU - Aastrup, Johannes
AU - Grimstrup, Jesper Møller
PY - 2016/9/12
Y1 - 2016/9/12
N2 - We present quantum holonomy theory, which is a non-perturbative theory of quantum gravity coupled to fermionic degrees of freedom. The theory is based on a (Formula presented.) -algebra that involves holonomy-diffeo-morphisms on a 3-dimensional manifold and which encodes the canonical commutation relations of canonical quantum gravity formulated in terms of Ashtekar variables. Employing a Dirac type operator on the configuration space of Ashtekar connections we obtain a semi-classical state and a kinematical Hilbert space via its GNS construction. We use the Dirac type operator, which provides a metric structure over the space of Ashtekar connections, to define a scalar curvature operator, from which we obtain a candidate for a Hamilton operator. We show that the classical Hamilton constraint of general relativity emerges from this in a semi-classical limit and we then compute the operator constraint algebra. Also, we find states in the kinematical Hilbert space on which the expectation value of the Dirac type operator gives the Dirac Hamiltonian in a semi-classical limit and thus provides a connection to fermionic quantum field theory. Finally, an almost-commutative algebra emerges from the holonomy-diffeomorphism algebra in the same limit.
AB - We present quantum holonomy theory, which is a non-perturbative theory of quantum gravity coupled to fermionic degrees of freedom. The theory is based on a (Formula presented.) -algebra that involves holonomy-diffeo-morphisms on a 3-dimensional manifold and which encodes the canonical commutation relations of canonical quantum gravity formulated in terms of Ashtekar variables. Employing a Dirac type operator on the configuration space of Ashtekar connections we obtain a semi-classical state and a kinematical Hilbert space via its GNS construction. We use the Dirac type operator, which provides a metric structure over the space of Ashtekar connections, to define a scalar curvature operator, from which we obtain a candidate for a Hamilton operator. We show that the classical Hamilton constraint of general relativity emerges from this in a semi-classical limit and we then compute the operator constraint algebra. Also, we find states in the kinematical Hilbert space on which the expectation value of the Dirac type operator gives the Dirac Hamiltonian in a semi-classical limit and thus provides a connection to fermionic quantum field theory. Finally, an almost-commutative algebra emerges from the holonomy-diffeomorphism algebra in the same limit.
UR - http://www.scopus.com/inward/record.url?scp=84987679939&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1504.07100
DO - 10.48550/arXiv.1504.07100
M3 - Article
AN - SCOPUS:84987679939
VL - 64
SP - 783
EP - 818
JO - Fortschritte der Physik
JF - Fortschritte der Physik
SN - 0015-8208
IS - 10
ER -