  This is the first of two papers on the superselection sectors of the
conformal model in the title, in a time zero formulation. A classification of
the sectors of the net of observables as restrictions of solitonic (twisted)
and non-solitonic (untwisted) sector automorphisms of proper extensions of the
observable net is given. All of them are implemented by the elements of a field
net in a non-regular vacuum representation and the existence of a global
compact Abelian gauge group is proved. A non-trivial center in the fixed-point
net of this gauge group appears, but in an unphysical representation and
reducing to the identity in the physical one. The completeness of the described
superselection structure, to which the second paper is devoted, is shown in
terms of Roberts' net cohomology. Some general features of physical field
models defined by twisted cross products of Weyl algebras in non-regular
representations are also presented.
