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Teoreticheskaya i Matematicheskaya Fizika, 2020, Volume 203, Number 2, Pages 220–230
DOI: https://doi.org/10.4213/tmf9872
(Mi tmf9872)
 

Quantization of the theory of half-differentiable strings

A. G. Sergeev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
References:
Abstract: The problem of quantizing the space $\Omega_d$ of smooth loops taking values in the $d$-dimensional vector space can be solved in the framework of the standard Dirac approach. But a natural symplectic form on $\Omega_d$ can be extended to the Hilbert completion of $\Omega_d$ coinciding with the Sobolev space $V_d:=H_0^{1/2}(\mathbb S^1,\mathbb R^d)$ of half-differentiable loops with values in $\mathbb R^d$. We regard $V_d$ as the phase space of the theory of half-differentiable strings. This theory can be quantized using ideas from noncommutative geometry.
Keywords: string theory, Connes quantization, quasisymmetric homeomorphism, universal Teichmüller space.
Funding agency Grant number
Russian Foundation for Basic Research 18-51-05009
19-01-00474
Russian Academy of Sciences - Federal Agency for Scientific Organizations
This research was supported in part by the Russian Foundation for Basic Research (Grant Nos. 18-51-05009 and 19-01-00474) and the Presidium of the Russian Academy of Sciences (Program “Nonlinear dynamics”).
Received: 11.05.2019
Revised: 11.05.2019
English version:
Theoretical and Mathematical Physics, 2020, Volume 203, Issue 2, Pages 621–630
DOI: https://doi.org/10.1134/S0040577920050050
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. G. Sergeev, “Quantization of the theory of half-differentiable strings”, TMF, 203:2 (2020), 220–230; Theoret. and Math. Phys., 203:2 (2020), 621–630
Citation in format AMSBIB
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    Теоретическая и математическая физика Theoretical and Mathematical Physics
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