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Quantization of the theory of half-differentiable strings
A. G. Sergeev Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
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.
Received: 11.05.2019 Revised: 11.05.2019
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
Linking options:
https://www.mathnet.ru/eng/tmf9872https://doi.org/10.4213/tmf9872 https://www.mathnet.ru/eng/tmf/v203/i2/p220
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Abstract page: | 301 | Full-text PDF : | 56 | References: | 33 | First page: | 10 |
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