Quantization of the~theory of half-differentiable strings
Teoretičeskaâ i matematičeskaâ fizika, Tome 203 (2020) no. 2, pp. 220-230
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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,
universal Teichmüller space.
Mots-clés : Connes quantization
Mots-clés : Connes quantization
@article{TMF_2020_203_2_a4,
author = {A. G. Sergeev},
title = {Quantization of the~theory of half-differentiable strings},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {220--230},
publisher = {mathdoc},
volume = {203},
number = {2},
year = {2020},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2020_203_2_a4/}
}
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/