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Erschienen in:
2019 | OriginalPaper | Buchkapitel
Quantization of Mathematical Theory of Non-Smooth Strings
verfasst von : A. G. Sergeev
Erschienen in: Geometric Methods in Physics XXXVI
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The mathematical problem of quantization of the theory of smooth strings consists of quantization of the space Ωd of smooth loops taking values in the d-dimensional Minkowski space Rd. The latter problem can be solved in frames of the standard Dirac approach. However, a natural symplectic form on Ωd may be extended to the Hilbert completion of Ωd coinciding with the Sobolev space Vd := H 0 1/2 (S1, Rd) of half-differentiable loops with values in Rd. So it is reasonable to consider Vd as the phase space of non-smooth string theory and try to quantize it. We explain how to do it using ideas from noncommutative geometry.