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New Trends in Mathematical and Theoretical Physics
October 3, 2016 15:00, Moscow, MIAN, Gubkina, 8
 


Quantization of Sobolev space of half-differentiable functions

Armen Sergeev

Steklov Mathematical Institute
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MP4 234.6 Mb

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Armen Sergeev
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Abstract: We shall construct the quantization of the Sobolev space $V=H_0^{1/2}(S^1,\mathbb R)$ of half-differentiable functions on the circle closely related to the string theory. The group $QS(S^1)$ of quasisymmetric homeomorphisms of the circle acts on this space by reparameterization but this action is not smooth. However, we can introduce a quantized infinitesimal action of $QS(S^1)$ on the Sobolev space $V$ which allows us to construct a quantum algebra of observables associated with the classical system $(V,QS(S^1))$.

Language: English

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