Spectrum Generating Affine Lie Algebras in Massive Field Theory

We present a new application of affine Lie algebras to massive quantum field theory in 2 dimensions, by investigating the q → 1 limit of the q-deformed affine ŝl(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 1, in the anti-periodic sector. The space of fields in the anti-periodic sector can be organized using level-1 highest weight representations, if one supplements the ŝl(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.