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This article is cited in 4 scientific papers (total in 4 papers)
Quantization of the Sobolev space of half-differentiable functions
A. G. Sergeev Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Abstract:
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, Dirac quantization.
Received: 14.02.2016 and 02.04.2016
Citation:
A. G. Sergeev, “Quantization of the Sobolev space of half-differentiable functions”, Mat. Sb., 207:10 (2016), 96–104; Sb. Math., 207:10 (2016), 1450–1457
Linking options:
https://www.mathnet.ru/eng/sm8673https://doi.org/10.1070/SM8673 https://www.mathnet.ru/eng/sm/v207/i10/p96
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Abstract page: | 623 | Russian version PDF: | 54 | English version PDF: | 5 | References: | 51 | First page: | 38 |
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