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Twistor quantization of open strings in three dimensions. (English) Zbl 0637.58041

An open string in Minkowski spacetime correspond to a quasi-periodic null curve. Such null curves have a natural twistor description when viewed as classical objects. This paper treats the first quantization of loops in real four-dimensional twistor space. Such loops corresponds to open strings in three-dimensional spacetime. The geometry and reality structures pertaining to twistors in three dimensions are reviewed and the twistor description of null geodesics is presented as a prototype for the discussion of null curves. The classical twistor structure of null curves is then described. The symplectic structure is exhibited and used to investigate the constraint algebra. Expressions for the momentum operators are found. The symplectic structure defines natural variables for covariant twistor quantization and the consequences of carrying this out are described. A twistor representation of the Virasoro algebra with central charge 2 is found and some solutions of the quantum constraints are exhibited.

MSC:

58Z05 Applications of global analysis to the sciences
81S10 Geometry and quantization, symplectic methods
83C45 Quantization of the gravitational field
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