Physics of Particles and Nuclei Letters

, Volume 11, Issue 7, pp 904–909 | Cite as

Quantization of universal Teichmüller space

  • Armen Sergeev


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 .


Nucleus Letter Group Diff Classical Observable Hamiltonian Vector Field Connes Quantization 
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Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteMoscowRussia

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