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Dual loop quantizations of 3d gravity | | Clement Delcamp
; Laurent Freidel
; Florian Girelli
; | | Date: |
8 Mar 2018 | | Abstract: | The loop quantization of 3d gravity consists in defining the Hilbert space of
states satisfying the Gau{ss} constraint and the flatness constraint. The
Gau{ss} constraint is enforced at the kinematical level by introducing spin
networks which form a basis for the Hilbert space of gauge invariant
functionals. The flatness constraint is implemented at the dynamical level via
the Ponzano-Regge state-sum model. We propose in this work a dual loop
quantization scheme where the role of the constraints is exchanged. The
flatness constraint is imposed first via the introduction of a new basis
labeled by group variables, while the Gau{ss} constraint is implemented
dynamically using a projector which is related to the Dijkgraaf-Witten model.
We discuss how this alternative quantization program is related to 3d
teleparallel gravity. | | Source: | arXiv, 1803.3246 | | Services: | Forum | Review | PDF | Favorites | |
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