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Quantum Symmetry Reduction for Diffeomorphism Invariant Theories
 of Connections, RWTH Aachen report PITHA 99/23, hepth/9907042
"... Given a symmetry group acting on a principal fibre bundle, symmetric states of the quantum theory of a diffeomorphism invariant theory of connections on this fibre bundle are defined. These symmetric states, equipped with a scalar product derived from the AshtekarLewandowski measure for loop quantu ..."
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Given a symmetry group acting on a principal fibre bundle, symmetric states of the quantum theory of a diffeomorphism invariant theory of connections on this fibre bundle are defined. These symmetric states, equipped with a scalar product derived from the AshtekarLewandowski measure for loop quantum gravity, form a Hilbert space of their own. Restriction to this Hilbert space yields a quantum symmetry reduction procedure in the framework of spin network states the structure of which is analyzed in detail. Three illustrating examples are discussed: Reduction of 3 + 1 to 2 + 1 dimensional quantum gravity, spherically symmetric quantum electromagnetism and spherically symmetric quantum gravity.
Gravitational collapse in loop quantum gravity, grqc/0610074; Leonardo Modesto, Quantum gravitational collapse
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Dynamics of scalar field in polymerlike representation
"... In recent twenty years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. We consider the quantum dynamics of a real massless scalar field coupled to gravity in this framework. A Hamiltonian operator for the scala ..."
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In recent twenty years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. We consider the quantum dynamics of a real massless scalar field coupled to gravity in this framework. A Hamiltonian operator for the scalar field can be well defined in the coupled diffeomorphism invariant Hilbert space, which is both selfadjoint and positive. On the other hand, the Hamiltonian constraint operator for the scalar field coupled to gravity can be well defined in the coupled kinematical Hilbert space. There are 1parameter ambiguities due to scalar field in the construction of both operators. The results heighten our confidence that there is no divergence within this background independent and diffeomorphism invariant quantization approach of matter coupled to gravity. Moreover, to avoid possible quantum anomaly, the master constraint programme can be carried out in this coupled system by employing a selfadjoint master constraint operator on the diffeomorphism invariant Hilbert space.
On the onset of inflation in loop quantum cosmology
"... Using a Liouville measure, similar to the one proposed recently by Gibbons and Turok, we investigate the probability that singlefield inflation with a polynomial potential can last long enough to solve the shortcomings of the standard hot big bang model, within the semiclassical regime of loop qua ..."
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Using a Liouville measure, similar to the one proposed recently by Gibbons and Turok, we investigate the probability that singlefield inflation with a polynomial potential can last long enough to solve the shortcomings of the standard hot big bang model, within the semiclassical regime of loop quantum cosmology. We conclude that, for such a class of inflationary models and for natural values of the loop quantum cosmology parameters, a successful inflationary scenario is highly improbable.
Oriented Matroids  Combinatorial Structures Underlying Loop Quantum Gravity
, 2010
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Semiclassical states in homogeneous loop quantum cosmology
 Class. Quantum Grav
, 2006
"... Semiclassical states in homogeneous loop quantum cosmology (LQC) are constructed by two different ways. In the first approach, we firstly construct an exponentiated annihilation operator. Then a kind of semiclassical (coherent) state is obtained by solving the eigenequation of that operator. Moreo ..."
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Semiclassical states in homogeneous loop quantum cosmology (LQC) are constructed by two different ways. In the first approach, we firstly construct an exponentiated annihilation operator. Then a kind of semiclassical (coherent) state is obtained by solving the eigenequation of that operator. Moreover, we use these coherent states to analyze the semiclassical limit of the quantum dynamics. It turns out that the Hamiltonian constraint operator employed currently in homogeneous LQC has correct classical limit with respect to the coherent states. In the second approach, the other kind of semiclassical state is derived from the mathematical construction of coherent states for compact Lie groups due to Hall.
Inflationary Quantum Cosmology: General Framework and Exact Bianchi I Solution
, 2004
"... Using the methods of loop quantum gravity, we derive a framework for describing an inflationary, homogeneous universe in a purely quantum theory. The classical model is formulated in terms of the AshtekarSen connection variables for a general subclass of Bianchi class A spacetimes. This formulation ..."
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Using the methods of loop quantum gravity, we derive a framework for describing an inflationary, homogeneous universe in a purely quantum theory. The classical model is formulated in terms of the AshtekarSen connection variables for a general subclass of Bianchi class A spacetimes. This formulation then provides a means to develop a corresponding quantum theory. An exact solution is derived for the classical Bianchi type I model and the corresponding semiclassical quantum state is found to also be an exact solution to the quantum theory. The development of a normalizable quantum state from this exact solution is presented and the implications for the normalizability of the Kodama state discussed. We briefly consider some consequences of such a quantum cosmological framework and show that the quantum scale factor of the universe has a continuous spectrum in this model. This result may suggest further modifications that are required to build a more accurate theory. We close this study by suggesting a variety of directions in which to take the results presented. 1