Geodesic
Quantization of the Sobolev space of half-differentiable functions
Sbornik. Mathematics, Tome 207 (2016) no. 10, pp. 1450-1457

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A quantization of the Sobolev space $V=H_0^{1/2}(S^1,\mathbb R)$ of half-differentiable functions on the circle, which is closely connected with string theory, is constructed. The group $\mathrm{QS}(S^1)$ of quasisymmetric circle homeomorphisms acts on $V$ by reparametrizations, but this action is not smooth. Nevertheless, a quantum infinitesimal action of $\mathrm{QS}(S^1)$ on $V$ can be defined, which enables one to construct a quantum algebra of observables which is associated with the system $(V,\mathrm{QS}(S^1))$. Bibliography: 7 titles.
Keywords: Sobolev space of half-differentiable functions, quasisymmetric homeomorphisms
Mots-clés : Dirac quantization. 
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     author = {A. G. Sergeev},
     title = {Quantization of the {Sobolev} space of half-differentiable functions},
     journal = {Sbornik. Mathematics},
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     publisher = {mathdoc},
     volume = {207},
     number = {10},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2016_207_10_a5/}
}
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A. G. Sergeev. Quantization of the Sobolev space of half-differentiable functions. Sbornik. Mathematics, Tome 207 (2016) no. 10, pp. 1450-1457. http://geodesic.mathdoc.fr/item/SM_2016_207_10_a5/