SPECTRUM GENERATING AFFINE LIE-ALGEBRAS IN MASSIVE FIELD-THEORY

We present a new application of affine Lie algebras to massive quantum field theory in two dimensions, by investigating the q --> 1 limit of the q-deformed affine sl(2) symmetry of the sine-Gordon theory, this limit occurring at the free fermion point. We describe how radial quantization leads to a quasi-chiral factorization of the space of fields. The conserved charges which generate the affine Lie algebra split into two independent affine algebras on this factorized space, each with level one, in the anti-periodic sector. The space of fields in the anti-periodic sector can be organized using level-one highest-weight representations, if one supplements the sl(2) algebra with the usual local integrals of motion. Using the integrals of motion, a momentum space bosonization involving vertex operators is formulated. This leads to a new way of computing form factors, as vacuum expectation values in momentum space.