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

Gerrit Handrich
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Gerrit Handrich: der Universität Freiburg, Fakultät für Physik

A chapter in Computer Algebra in Scientific Computing CASC’99, 1999, pp 229-232 from Springer

Abstract: 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.

Keywords: Poisson Bracket; Associative Algebra; Poisson Algebra; Cautious Approach; Quantum Algebra (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1007/978-3-642-60218-4_17

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