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Mat. Sb., 2016, Volume 207, Number 10, Pages 96–104 (Mi msb8673)  

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.

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).


DOI: https://doi.org/10.4213/sm8673

Full text: PDF file (688 kB)
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English version:
Sbornik: Mathematics, 2016, 207:10, 1450–1457

Bibliographic databases:

UDC: 517.98
MSC: 30C62, 81T30
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

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. G. Sergeev, “Quantum Calculus and Quasiconformal Mappings”, Math. Notes, 100:1 (2016), 123–131  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. A. G. Sergeev, “Spin Geometry of Dirac and Noncommutative Geometry of Connes”, Proc. Steklov Inst. Math., 298 (2017), 256–293  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. Sergeev A.G., “Quantization of the Sobolev Space of Half-Differentiable Functions, II”, Russ. J. Math. Phys., 26:3 (2019), 401–405  crossref  mathscinet  zmath  isi
    4. A. G. Sergeev, “In search of infinite-dimensional Kähler geometry”, Russian Math. Surveys, 75:2 (2020), 321–367  mathnet  crossref  crossref  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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