(2+1) sector of (3+1) gravity
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In this article, the rank-2 sector of classical (3 + 1)-dimensional Ashtekar gravity is considered and it is found that the consistency of the evolution equations with the reality of the volume requires that the 3-surface of initial data is foliated by 2-surfaces tangential to degenerate triads.Abstract:
The rank-2 sector of classical (3 + 1)-dimensional Ashtekar gravity is considered. It is found that the consistency of the evolution equations with the reality of the volume requires that the 3-surface of initial data is foliated by 2-surfaces tangential to degenerate triads. In turn, the degeneracy is preserved by the evolution. The 2-surfaces behave like (2 + 1)-dimensional empty spacetimes with a massless complex field propagating along each of them. The results provide some evidence for the issue of evolving a non-degenerate gravitational field into a degenerate sector of Ashtekar's phase space.read more
Citations
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Background independent quantum gravity: A Status report
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Quantum gravity as a Fermi liquid
TL;DR: In this article, a reformulation of loop quantum gravity with a cosmological constant and no matter as a Fermi-liquid theory is presented, where the Chern-Simons state reduces to Jacobson's degenerate sector describing 1+1 dimensional propagating fermions with nonlocal interactions.
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Quantum Gravity as a Fermi Liquid
TL;DR: In this article, a reformulation of loop quantum gravity with a cosmological constant and no matter as a Fermi-liquid theory is presented, where the Chern-Simons state reduces to Jacobson's degenerate sector describing 1+1 dimensional propagating fermions with nonlocal interactions.
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Towards the self-adjointness of a Hamiltonian operator in loop quantum gravity
TL;DR: In this article, the authors attack the open issue of the physical Hamiltonian operator's property in the deparameterized model of loop quantum gravity coupled to a scalar field, and show that the operator is essentially self-adjoint.
Journal ArticleDOI
Degenerate metric phase boundaries
Ingemar Bengtsson,Ted Jacobson +1 more
TL;DR: In this article, the structure of boundaries between degenerate and non-degenerate solutions of Ashtekar's canonical reformulation of Einstein's equations is studied, and it is shown that degenerate phase boundaries are always null.
References
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New variables for classical and quantum gravity.
Abhay Ashtekar,Abhay Ashtekar +1 more
TL;DR: A Hamiltonian formulation of general relativity based on certain spinorial variables is introduced that enables one to imbed the constraint surface in the phase space of Einstein's theory into that of Yang-Mills theory.
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New Hamiltonian formulation of general relativity
TL;DR: An important feature of the new form of constraints is the natural embedding of the constraint surface of the Einstein phase space into that of Yang-Mills phase space, which provides new tools to analyze a number of issues in both classical and quantum gravity.
Book
Lectures on Non-Perturbative Canonical Gravity
TL;DR: In this article, the authors present an up-to-date account of a non-perturbative, canonical quantization program for gravity, which was highlighted in virtually every major conference in gravitational physics over the past three years.
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The cosmological constants
TL;DR: In this paper, the connection between the lagrangian and the hamiltonian is partially worked out, and it is shown how to identify the space-time metric in terms of them.
Journal ArticleDOI
New constraints for canonical general relativity
TL;DR: In this article, a fully 4-diffeo invariant canonical theory in Ashtekar's variables, derived from Plebanski's action, was shown to be invariant under a number of new constraints.