Quantization of the \(G\)-connections via the tangent groupoid (Q2855838)
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scientific article; zbMATH DE number 6218013
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Quantization of the \(G\)-connections via the tangent groupoid |
scientific article; zbMATH DE number 6218013 |
Statements
22 October 2013
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quantum gravity
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canonical gravity
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Hamiltonian
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Ashtekar
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loop variables
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quantization
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\(G\)-connections
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tangent groupoid
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Quantization of the \(G\)-connections via the tangent groupoid (English)
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Let \(G\) be a compact Lie group and \(\Sigma \) a compact oriented manifold. The space of \(G\)-connections is described using the tangent grupoid \(\mathcal{T}\Sigma \). By adding a Riemannian metric on \(\Sigma \) the \(G\)-connections are obtained as integral kernels and the tetrads are formulated as Dirac-type operators. It is proved that such a procedure is in fact a quantization by remarking that the classical limit of their quantum interaction, the commutator, gives back their classical interaction, namely the Poisson bracket.
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