Geodesic
Quantization of the theory of half-differentiable strings
Teoretičeskaâ i matematičeskaâ fizika, Tome 203 (2020) no. 2, pp. 220-230 Cet article a éte moissonné depuis la source Math-Net.Ru

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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, quasisymmetric homeomorphism
Mots-clés : Connes quantization, universal Teichmüller space. 
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A. G. Sergeev. Quantization of the theory of half-differentiable strings. Teoretičeskaâ i matematičeskaâ fizika, Tome 203 (2020) no. 2, pp. 220-230. http://geodesic.mathdoc.fr/item/TMF_2020_203_2_a4/

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