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Sbornik: Mathematics, 2016, Volume 207, Issue 10, Pages 1450–1457
DOI: https://doi.org/10.1070/SM8673
(Mi sm8673)
 

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
References:
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.
Funding agency Grant number
Russian Science Foundation 14-50-00005
This research was supported by a grant of the Russian Science Foundation (project no. 14-50-00005).
Received: 14.02.2016 and 02.04.2016
Russian version:
Matematicheskii Sbornik, 2016, Volume 207, Number 10, Pages 96–104
DOI: https://doi.org/10.4213/sm8673
Bibliographic databases:
Document Type: Article
UDC: 517.98
MSC: 30C62, 81T30
Language: English
Original paper language: Russian
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
Citation in format AMSBIB
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  • https://doi.org/10.1070/SM8673
  • https://www.mathnet.ru/eng/sm/v207/i10/p96
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник Sbornik: Mathematics
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    Abstract page:668
    Russian version PDF:61
    English version PDF:9
    References:57
    First page:38
     
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