AFFINE LIE-ALGEBRAS IN MASSIVE FIELD-THEORY AND FORM-FACTORS FROM VERTEX OPERATORS

We present a new application of affine Lie algebras to massive quantum field theory in 2 dimensions by investigating the q --> 1 limit of th e q-deformed affine <(sl(2))over cap> symmetry of the sine-Gordon theo ry, this limit occurring at the free fermion point. Working in radial quantization leads to a quasi-chiral factorization of the space of fie lds. The conserved charges which generate the aff ne Lie algebra split into two independent affine algebras on this factorized space, each w ith level 1 in the anti-periodic sector, and level 0 in the periodic s ector. The space of fields in the anti-periodic sector can be organize d using level-1 highest weight representations if one supplements the <(sl(2))over cap> algebra with the usual local integrals of motion. in troducing a particle-field duality leads to a new way of computing for m-factors in radial quantization. Using the integrals of motion, a mom entum space bosonization involving vertex operators is formulated. For m-factors are computed as vacuum expectation values of vertex operator s in momentum space.