Asymptotic properties of the quantum representations of the modular group (Q2844732)
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scientific article; zbMATH DE number 6199342
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Asymptotic properties of the quantum representations of the modular group |
scientific article; zbMATH DE number 6199342 |
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Asymptotic properties of the quantum representations of the modular group (English)
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19 August 2013
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0.9536441
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0.9240146
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0.91916347
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0.9093003
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0.90366125
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Quantum Chern-Simons theory developed by Witten-Reshetikhin-Turaev has a semi-classical limit, where the level plays the role of the inverse of the Planck constant. The characters of the quantum representation of the modular group are the three dimensional invariants of the torus bundles. The author proves that the trace of a Fourier integral operator has an asymptotic expansion, which recovers Jeffrey's result [\textit{L. C. Jeffrey}, Commun. Math. Phys. 147, No. 3, 563--604 (1992; Zbl 0755.53054)]. The proofs are completely different and the result is more general in that the author treats any hyperbolic element with any simple and simply connected group \(G\).
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