Representation of Fields in a Two-Dimensional Model Theory

Abstract

The two‐dimensional model recently suggested by Schroer is examined. The free scalar massless field in two dimensions is discussed in detail. The infrared‐myriotic representations of this field which arise in the model are described; it is shown that, up to unitary equivalence, the required representation depends only on the net total charge of the fermions. Discussion is also given of distribution‐theoretic aspects of the fields, and in particular, of possible restrictions on test functions.