| We present three different pieces of work done while a graduate student at the State University of New York at Stony Brook.;The first one deals with the relation between conformal invariance and integrability in two-dimensional field theories. It is shown that a well known test for integrability, the factorization of tree level scattering amplitudes, fails in the case of massless theories. It is also suggested that this actually tests the decoupling between left- and right-movers in massless (conformally invariant) models. Three examples are presented: the O(n) model, the Wess-Zumino-Witten model, and an hyperkahler supersymmetric model.;The second piece is a collaboration in which we diagonalized numerically the frustrated Heisenberg spin-;The third and last piece concerns the representations, in a fermionic Fock space, of the algebra of diffeomorphisms of the n-torus for n... |
