Deformation Operators of Spin Networks and Coarse-Graining
Oct 12, 201331 pages
Published in:
- Class.Quant.Grav. 31 (2014) 075004
- Published: Mar 5, 2014
e-Print:
- 1310.3362 [gr-qc]
View in:
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Abstract: (IOP)
In the context of loop quantum gravity, quantum states of geometry are mathematically defined as spin networks living on graphs embedded in the canonical space-like hypersurface. In the effort to study the renormalization flow of loop gravity, a necessary step is to understand the coarse-graining of these states in order to describe their relevant structure at various scales. Using the spinor network formalism to describe the phase space of loop gravity on a given graph, we focus on a bounded (connected) region of the graph and coarse-grain it to a single vertex using a gauge-fixing procedure. We discuss the ambiguities in the gauge-fixing procedure and its consequences for coarse-graining spin(or) networks. This allows to define the boundary deformations of that region in a gauge-invariant fashion and to identify the area preserving deformations as U(N) transformations similarly to the already well-studied case of a single intertwiner. The novelty is that the closure constraint is now relaxed and the closure defect interpreted as a local measure of the curvature inside the coarse-grained region. It is nevertheless possible to cancel the closure defect by a Lorentz boost. We further identify a Lorentz-invariant observable related to the area and closure defect, which we name ‘rest area’. Its physical meaning remains an open issue.Note:
- 24 pages
- 04.60.Pp
- 04.60.Nc
- loop quantum gravity
- spin network
- spinor network
- gauge fixing
- coarse-graining
- quantum gravity: loop space
- spin: network
- operator: deformation
References(55)
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