Factorized Smatrices in two dimensions as the exact solutions of certain relativistic quantum field theory models
Abstract
The general properties of the factorized Smatrix in twodimensional spacetime are considered. The relation between the factorization property of the scattering theory and the infinite number of conservation laws of the underlying field theory is discussed. The factorization of the total Smatrix is shown to impose hard restrictions on twoparticle matrix elements: they should satisfy special identities, the socalled factorization equations. The general solution of the unitarity, crossing and factorization equations is found for the Smatrices having isotopic O(N)symmetry. The solution turns out to have different properties for the cases N = 2 and N ⩾ 3. For N = 2 the general solution depends on one parameter (of coupling constant type), whereas the solution for N ⩾ 3 has no parameters but depends analytically on N. The solution for N = 2 is shown to be an exact soliton Smatrix of the sineGordon model (equivalently the massive Thirring model). The total Smatrix of the model is constructed. In the case of N ⩾ 3 there are two "minimum" solutions, i.e., those having a minimum set of singularities. One of them is shown to be an exact S matrix of the quantum O(N)symmetric nonlinear σmodel, the other is argued to describe the scattering of elementary particles of the GrossNeveu model.
 Publication:

Annals of Physics
 Pub Date:
 August 1979
 DOI:
 10.1016/00034916(79)903919
 Bibcode:
 1979AnPhy.120..253Z