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Relating loop quantum cosmology to loop quantum gravity: Symmetric sectors and embeddings

Jonathan Engle
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Abstract

In this paper we address the meaning of states in loop quantum cosmology (LQC), in the context of loop quantum gravity. First, we introduce a rigorous formulation of an embedding proposed by Bojowald and Kastrup, of LQC states into loop quantum gravity. Then, using certain holomorphic representations, a new class of embeddings, called b-embeddings, are constructed, following the ideas of [1]. We exhibit a class of operators preserving each of these embeddings, and show their consistency with the LQC quantization. In the b-embedding case, the classical analogues of these operators separate points in phase space. Embedding at the gauge and diffeomorphism invariant level is discussed briefly in the conclusions.

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Jonathan Engle. 2007-12-28. Relating loop quantum cosmology to loop quantum gravity: Symmetric sectors and embeddings. https://doi.org/10.1088/0264-9381%2F24%2F23%2F004

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