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Quantization by Presentation: The Nambu-Goto String in 1+3 Dimensions

In: Computer Algebra in Scientific Computing CASC’99

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  • Gerrit Handrich

    (der Universität Freiburg, Fakultät für Physik)

Abstract

In a cautious approach to the quantization of the Nambu-Goto string in 1+3 dimensions, correspondence is required for the algebra of observables only. With the help of a presentation of this Poisson algebra the associative quantum algebra may be constructed. A defining relation of the Poisson algebra determines one of the quantum algebra up to a finite number of terms of higher order in ħ. These terms are severely restricted when one requires the correct classical limit for all the relations implied by the defining ones. The ideal generated by the associative defining relations has been computed up to degree five with the help of Mathematica routines specially designed to make use of the so(3) representation space structure of the algebra. These computations strongly support the consistency of the correspondence postulate for the algebra of observables.

Suggested Citation

  • Gerrit Handrich, 1999. "Quantization by Presentation: The Nambu-Goto String in 1+3 Dimensions," Springer Books, in: Victor G. Ganzha & Ernst W. Mayr & Evgenii V. Vorozhtsov (ed.), Computer Algebra in Scientific Computing CASC’99, pages 229-232, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-60218-4_17
    DOI: 10.1007/978-3-642-60218-4_17
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