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Harmonic analysis of the relativistic string in spinorial coordinates. (English) Zbl 0731.43007

The finite-harmonic solution of the constraint equations of the spinor representation of the relativistic string is presented. The harmonic decomposition is made in the form of a product representation. A recursive method for relating series and product parameters is described. The generalization for the infinite harmonic case and the problem of quantization are discussed. It is suggested that the physical degrees of freedom of a finite harmonic string might not match up with those of the infinite harmonic string in the limit \(N\to \infty\). Consequently, the critical dimension could be different from that for the usual string theories.

MSC:

43A99 Abstract harmonic analysis
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81R25 Spinor and twistor methods applied to problems in quantum theory
83E30 String and superstring theories in gravitational theory
53C27 Spin and Spin\({}^c\) geometry
53B50 Applications of local differential geometry to the sciences
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