@phdthesis{Koslowski2008,
  author    = {Koslowski, Tim Andreas},
  title     = {Cosmological Sectors in Loop Quantum Gravity},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-28244},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2008},
  abstract  = {This thesis is concerned with the description of macroscopic geometries through Loop Quantum Gravity, and there particularly with the description of cosmology within full Loop Quantum Gravity. For this purpose we depart from two distinct (classically virtually equivalent) ans{\"a}tze: One is phase space reduction and the other is the restriction to particular states. It turns out that the quantum analogue of these two approaches are fundamentally different: The quantum analogue of phase space reduction needs the reformulation in terms of the observable Poisson algebra, so it can be applied to the noncommutative quantum phase space: It rests on the observation that the observable Poisson algebra of classical canonical cosmology is induced by the embedding of the reduced cosmological phase space into the phase space of full General Relativity. Using techniques related to Rieffel-induction, we develop a construction for a noncommutative embedding that has a classical limit that is described by a Poisson embedding. To be able to use this class of noncommutative embeddings for Loop Quantum Gravity, one needs a complete group of diffeomorphisms for the quantum theory, which is constructed. These two results are applied to construct a quantum embedding of a cosmological sector into full Loop Quantum Gravity. The embedded cosmological sector turns out to be discrete, like standard Loop Quantum Cosmology and can be interpreted as a super-selection sector thereof; however due to pathologies of the dynamics of full Loop Quantum Gravity, one can not induce a meaningful dynamics for this cosmological sector. The quantum analogue of restricting the space of states is achieved by explicitly constructing states for Loop Quantum Gravity with smooth geometry. These states do not exist within the Hilbert space of Loop Quantum Gravity, but as states on the observable algebra of Loop Quantum Gravity. This observable algebra is built from spin network functions, area operators and a restricted set of fluxes. For this algebra to be physically complete, we needed to construct a version of Loop Quantum Geometry based on a fundamental area operator. This version of Loop Quantum Geometry is constructed. Since the smooth geometry states are not in the Hilbert space of standard Loop Quantum Gravity, we needed to calculate the Hilbert space representation that contains them using the GNS construction. This representation of the observable algebra can be illustrated as a classical condensate of geometry with quantum fluctuations thereon. Using these representations we construct a quantum-minisuperspace, which allows for an interpretation of standard Loop Quantum Cosmology in terms of these states and led us to conjecture a new approach for the implementation of dynamics for Loop Quantum Gravity.},
  subject      = {Gravitation},
  language  = {en}
}