Topological limit of gravity admitting an SU(2) connection formulation (original) (raw)
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Quantum gravity in terms of topological observables
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We recast the action principle of four dimensional General Relativity so that it becomes amenable for perturbation theory which doesn't break general covariance. The coupling constant becomes dimensionless (G N ewton Λ) and extremely small 10 −120 . We give an expression for the generating functional of perturbation theory. We show that the partition function of quantum General Relativity can be expressed as an expectation value of a certain topologically invariant observable. This sets up a framework in which quantum gravity can be studied perturbatively using the techniques of topological quantum field theory. *
A Starodubtsev, Quantum gravity in terms of topological observables
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We recast the action principle of four dimensional General Relativity so that it becomes amenable for perturbation theory which doesn’t break general covariance. The coupling constant becomes dimensionless (GNewtonΛ) and extremely small 10 −120. We give an expression for the generating functional of perturbation theory. We show that the partition function of quantum General Relativity can be expressed as an expectation value of a certain topologically invariant observable. This sets up a framework in which quantum gravity can be studied perturbatively using the techniques of topological quantum field theory. 1
The European Physical Journal C
By applying the Faddeev-Jackiw symplectic approach we systematically show that both the local gauge symmetry and the constraint structure of topologically massive gravity with a cosmological constant , elegantly encoded in the zero-modes of the symplectic matrix, can be identified. Thereafter, via a suitable partial gauge-fixing procedure, the time gauge, we calculate the quantization bracket structure (generalized Faddeev-Jackiw brackets) for the dynamic variables and confirm that the number of physical degrees of freedom is one. This approach provides an alternative to explore the dynamical content of massive gravity models. CyT under grand number CB-2014-01/240781. We would like to thank G. Tavares-Velasco for reading a draft version of this paper and alerting us to various typos.
Continuous formulation of the loop quantum gravity phase space
In this paper, we study the discrete classical phase space of loop gravity, which is expressed in terms of the holonomy-flux variables, and show how it is related to the continuous phase space of general relativity. In particular, we prove an isomorphism between the loop gravity discrete phase space and the symplectic reduction of the continuous phase space with respect to a flatness constraint. This gives for the first time a precise relationship between the continuum and holonomy-flux variables. Our construction shows that the fluxes depend on the three-geometry, but also explicitly on the connection, explaining their non commutativity. It also clearly shows that the flux variables do not label a unique geometry, but rather a class of gauge-equivalent geometries. This allows us to resolve the tension between the loop gravity geometrical interpretation in terms of singular geometry, and the spin foam interpretation in terms of piecewise flat geometry, since we establish that both geometries belong to the same equivalence class. This finally gives us a clear understanding of the relationship between the piecewise flat spin foam geometries and Regge geometries, which are only piecewiselinear flat: While Regge geometry corresponds to metrics whose curvature is concentrated around straight edges, the loop gravity geometry correspond to metrics whose curvature is concentrated around not necessarily straight edges. * Electronic address: lfreidel@perimeterinstitute.ca † Electronic address: mgeiller@apc.univ-paris7.fr ‡ Electronic address: jziprick@perimeterinstitute.ca