Eur. Phys. J. C 16, 303-310
DOI 10.1007/s100520000428
The diagonalisation of the Lund fragmentation model I
Department of Theoretical Physics, Lund University,
Sölvegatan 14A, 22362 Lund, Sweden
Received: 7 April 2000 / Published online: 18 May 2000 - © Springer-Verlag 2000
Abstract
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