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Discreteness of area and volume in quantum gravity [Nucl. Phys. B 442 (1995) 593]
Abstract We study the operator that corresponds to the measurement of volume, in non-perturbative quantum gravity, and we compute its spectrum. The operator is constructed in the loop representation,Expand
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Lorentz invariance with an invariant energy scale.
We propose a modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertialExpand
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Gravity's Rainbow
Non-linear special relativity (or doubly special relativity) is a simple framework for encoding properties of flat quantum space-time. In this paper we show how this formalism may be generalized toExpand
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A theory of everything?
In his later years, Einstein sought a unified theory that would extend general relativity and provide an alternative to quantum theory. There is now talk of a ‘theory of everything’ (althoughExpand
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Principle of relative locality
We propose a deepening of the relativity principle according to which the invariant arena for nonquantum physics is a phase space rather than spacetime. Descriptions of particles propagating andExpand
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Loop space representation of quantum general relativity
Abstract We define a new representation for quantum general relativity, in which exact solutions of the quantum constraints may be obtained. The representation is constructed by means of aExpand
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Generalized Lorentz invariance with an invariant energy scale
The hypothesis that the Lorentz transformations may be modified at Planck scale energies is further explored. We present a general formalism for theories which preserve the relativity of inertialExpand
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Quantum gravity with a positive cosmological constant
A quantum theory of gravity is described in the case of a positive cosmological constant in 3 + 1 dimensions. Both old and new results are described, which support the case that loop quantum gravityExpand
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Linking topological quantum field theory and nonperturbative quantum gravity
Quantum gravity is studied nonperturbatively in the case in which space has a boundary with finite area. A natural set of boundary conditions is studied in the Euclidean signature theory in which theExpand
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The case for background independence
The aim of this paper is to explain carefully the arguments behind the assertion that the correct quantum theory of gravity must be background independent. We begin by recounting how the debateExpand
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