  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 breakup 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 corresponds to the momentum transfers between the produced particles)
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 time-like 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.
