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Journal Articles Classical and Quantum Gravity Year : 2007

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

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.

Dates and versions

hal-00176052 , version 1 (02-10-2007)

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Jonathan Engle. Relating loop quantum cosmology to loop quantum gravity: Symmetric sectors and embeddings. Classical and Quantum Gravity, 2007, 24 (23), pp.5777. ⟨hal-00176052⟩
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