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Particles and Fields

Eur. Phys. J. C 16, 303-310
DOI 10.1007/s100520000428

The diagonalisation of the Lund fragmentation model I

B. Andersson - F. Söderberg

Department of Theoretical Physics, Lund University, Sölvegatan 14A, 22362 Lund, Sweden

Received: 7 April 2000 / Published online: 18 May 2000 - © Springer-Verlag 2000

We will in this note show that it is possible to diagonalise the Lund fragmentation model. We show that the basic original result, the Lund area law, can be factorised into a product of transition operators, each describing the production of a single particle and the two adjacent break up points (vertex positions) of the string field. The transition operator has a discrete spectrum of (orthonormal) eigenfunctions, describing the vertex positions (which in a dual way correspond to the momentum transfers between the particles produced) and discrete eigenvalues, which only depend upon the particle produced. The eigenfunctions turn out to be the well-known two-dimensional harmonic oscillator functions and the eigenvalues are the analytic continuations of these functions to timelike values (corresponding to the particle mass). In this way all observables in the model can be expressed in terms of analytical formulas. In this note only the 1+1-dimensional version of the model is treated, but we end with remarks on the extensions to gluonic radiation, transverse momentum generation etc., to be performed in future papers.

Copyright Società Italiana di Fisica, Springer-Verlag 2000