Nonlocal charges in two dimensions

Abstract

We exhibit some correspondences between known properties of local charges and the properties of nonlocal charges in the $\mathrm{O}\mathrm{}\left(n\right)\mathrm{}$ $\sigma$ model in two dimensions. By determining the magnitudes of the matrix elements of the nonlocal charges between one-particle states and using their multiplicative action on asymptotic multiparticle states, one sees that production is forbidden for essentially the same reason that an infinite number of local conservation laws forbid production. The way that continuation to $n=2\mathrm{}$ may correspond to the massive Thirring model at $g=-\frac{\pi }{2}$ is briefly discussed.