The operator solution of the anomalous chiral Schwinger model is discu
ssed on the basis of the: general principles of Wightman field theory.
Some basic structural properties of the model are analyzed taking a c
areful control on the Hilbert space associated with the Wightman funct
ions. The isomorphism between gauge noninvariant and gauge invariant d
escriptions of the anomalous theory is established in terms of the cor
responding field algebras. We show that (i) the Theta-vacuum represent
ation and (ii) the suggested equivalence of vector Schwinger model and
chiral Schwinger model cannot be established in terms of the intrinsi
c field algebra. (C) 1997 Academic Press.