We discuss the twistor quantization problem for the classical system (Vd,Ad), represented by the phase space Vd, identified with the Sobolev space H01/2 (S1,ℝd) of half-differentiable vector functions on the circle, and the algebra of observables Ad, identified with the semi-direct product of the Heisenberg algebra of Vd and the algebra Vect(S1) of tangent vector fields on the circle.
twistor quantization Sobolev space of half-differentiable functions group of diffeomorphisms of the circle
58E20 53C28 32L25
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Bowick M J, Rajeev S G. The holomorphic geometry of closed bosonic string theory and Diff S1/S1. Nucl Phys, B293: 348–384 (1987)CrossRefMathSciNetGoogle Scholar
Davidov J, Sergeev A G. Twistor quantization of loop spaces. Proc Steklov Inst Math, 217: 1–90 (1997)MathSciNetGoogle Scholar
Sergeev A G. Kähler Geometry of Loop Spaces (in Russian). Moscow: Moscow Centre for Continuous Math Education, 2001Google Scholar
Kobayashi S, Nomizu K. Foundations of Differential Geometry. New York-London: Interscience Publishers, 1963MATHGoogle Scholar