Quantization of universal Teichmüller space
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Universal Teichmüller space Open image in new window is the quotient of the group QS(S 1) of quasisymmetric homeomorphisms of S 1 modulo Möbius transformations. The quantization problem for Open image in new window arises in the theory of non-smooth closed bosonic strings. Because of non-smoothness of strings the natural QS(S 1)-action on Open image in new window is also not smooth so there is no classical Lie algebra, associated to QS(S 1). However, using methods of non-commutative geometry, we can define a quantum Lie algebra of observables Der q (QS), yielding the quantization of Open image in new window .
KeywordsNucleus Letter Group Diff Classical Observable Hamiltonian Vector Field Connes Quantization
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- 5.A. G. Sergeev, Lectures on the Universal Teichmüller Space (Steklov Mathematical Institute, Moscow, 2013).Google Scholar