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2011

Towards lattice-regularized Quantum Gravity

Diakonov, Dmitri

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Using the Cartan formulation of General Relativity, we construct a well defined lattice-regularized theory capable to describe large non-perturbative quantum fluctuations of the frame field (or the metric) and of the spin connection.

To that end we need to present the tetrad by a composite field built as a bilinear combination of fermion fields.
The theory is explicitly invariant under local Lorentz transformations and, in the continuum limit, under general covariant transformations, or diffeomorphisms.
Being well defined for large and fast varying fields at the ultraviolet cutoff, the theory simultaneously has chances of reproducing standard General Relativity in the infrared continuum limit.

Towards lattice-regularized Quantum Gravity · Around

Built on

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P. C. Nelson, Phys. Lett. A 79
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Similar

E. Cartan, Sur les variétés à connexion affine, et la théorie de la relativitè généralisée (première partie)
1986
Cited alongside, same era.
H. Weyl, Z. Phys. 56
1986
Cited alongside, same era.
G.E. Volovik, Physica B162
1990
Cited alongside, same era.
D. Diakonov, A. G. Tumanov and A. A. Vladimirov, arXiv:1104.2432 [hep-th]
Original
Cited in the paper.
P. Baekler and F. W. Hehl, arXiv:1105.3504 [gr-qc]
Original
Cited in the paper.
K. Akama, Prog. Theor. Phys. 60
Cited in the paper.
C. Wetterich, arXiv:1108.1313 [hep-th]
Original
Cited in the paper.
In Ref. [ 8 ] local Lorentz symmetry is achieved despite the wrong transformation properties of the frame field, by taking a specific action
Cited in the paper.

Then

A. Zee, Quantum Field Theory in a Nutshell
2003
Later among the works it cites.
V. Fock and D. Iwanenko, C. R. Acad. Sci., Paris 188
2004
Later among the works it cites.
C. Wetterich, Phys. Rev. Lett. 94
2005
Later among the works it cites.

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