Abstract
We construct certain non-Fock representations of the canonical commutation relations for the zero-mass scalar field in two-dimensional space-time. These are obtained from the free-field representation by applying localised automorphisms, are strongly locally Fock, and have a positive energy-momentum spectrum. The model is suggested by an early paper of Skyrme, and provides a concrete example of the algebraic theory of observables and charges. It satisfies some, but not all, of the postulates of Doplicher, Haag and Roberts. The Bose-Fermi alternative does not hold: instead, we find a continuum of representations which interpolates between the Bose and Fermi sectors. We are able to construct the local field algebra, which provides a unitary multiplier representation of a gauge group of the second kind.
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