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Separable Hilbert space in loop quantum gravity [PDF]
Journal of Mathematical Physics, 2004 We study the separability of the state space of loop quantum gravity. In the standard construction, the kinematical Hilbert space of the diffeomorphism-invariant states is nonseparable. This is a consequence of the fact that the knot space of the equivalence classes of graphs under diffeomorphisms is noncountable.
Fairbairn, Winston, Rovelli, Carlo
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On the space of generalized fluxes for loop quantum gravity [PDF]
Classical and Quantum Gravity, 2013 We show that the space of generalized fluxes - momentum space - for loop quantum gravity cannot be constructed by Fourier transforming the projective limit construction of the space of generalized connections - position space - due to the non-abelianess of the gauge group SU(2).
Dittrich, B., Guedes, C., Oriti, D.
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Loop quantum gravity on non-compact spaces [PDF]
Nuclear Physics B, 2000 We present a general procedure for constructing new Hilbert spaces for loop quantum gravity on non-compact spatial manifolds. Given any fixed background state representing a non-compact spatial geometry, we use the Gel'fand-Naimark-Segal construction to obtain a representation of the algebra of observables.
Matthias Arnsdorf, Sameer Gupta
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Continuous formulation of the loop quantum gravity phase space [PDF]
Classical and Quantum Gravity, 2013 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 ...
Laurent Freidel +3 more
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Projective loop quantum gravity. I. State space [PDF]
Journal of Mathematical Physics, 2016 81 pages, many ...
Thomas Thiemann +2 more
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One-loop quantum gravity in Schwarzschild space-time [PDF]
Physical Review D, 1995 The quantum theory of linearized perturbations of the gravitational field of a Schwarzschild black hole is presented. The fundamental operators are seen to be the perturbed Weyl scalars $\dot _0$ and $\dot _4$ associated with the Newman-Penrose description of the classical theory.
Adrian C. Ottewill +2 more
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Space and Time in Loop Quantum Gravity [PDF]
, 2020 Contribution to the volume "Beyond Spacetime: The Philosophical Foundations of Quantum Gravity", edited by Baptiste Le Biha, Keizo Matsubara and Christian ...
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Real alternative to quantum gravity in loop space [PDF]
Physical Review D, 1996 11 pages, plain TeX, Feb ...
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LOOP QUANTUM GRAVITY AND ASYMPTOTICALLY FLAT SPACES [PDF]
The Ninth Marcel Grossmann Meeting, 2002 After motivating why the study of asymptotically flat spaces is important in loop quantum gravity, we review the extension of the standard framework of this theory to the asymptotically flat sector based on the GNS construction. In particular, we provide a general procedure for constructing new Hilbert spaces for loop quantum gravity on non-compact ...
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Algebraic quantum gravity (AQG): IV. Reduced phase space quantization of loop quantum gravity [PDF]
Classical and Quantum Gravity, 2010 We perform a canonical, reduced phase space quantisation of General Relativity by Loop Quantum Gravity (LQG) methods. The explicit construction of the reduced phase space is made possible by the combination of 1. the Brown -- Kuchar mechanism in the presence of pressure free dust fields which allows to deparametrise the theory and 2.
Giesel, K., Thiemann, T.
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